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FNV Hash
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FNV quick index


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FNV hash history

The basis of the FNV hash algorithm was taken from an idea sent as reviewer comments to the IEEE POSIX P1003.2 committee by Glenn Fowler and Phong Vo back in 1991. In a subsequent ballot round: Landon Curt Noll improved on their algorithm. Some people tried this hash and found that it worked rather well. In an Email message to Landon, they named it the ``Fowler/Noll/Vo'' or FNV hash.

FNV hashes are designed to be fast while maintaining a low collision rate. The FNV speed allows one to quickly hash lots of data while maintaining a reasonable collision rate. The high dispersion of the FNV hashes makes them well suited for hashing nearly identical strings such as URLs, hostnames, filenames, text, IP addresses, etc.

The IETF has an informational draft on The FNV Non-Cryptographic Hash Algorithm

The FNV hash is in wide spread use:

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CC0 - Public Domain

FNV hash algorithms and source code been been put into the public domain via the following Creative Commons license:

CC0 1.0 Universal (CC0 1.0) Public Domain Dedication

No Copyright - CC0 - No Rights Reserved

CC0 Public Domain

The CC0 license means that the hash algorithms and source code has been dedicated to the public domain by waiving all of our rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.

You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

See the Creative Commons CC0 page for more details.

We did NOT patent FNV

The authors of the FNV algorithm took deliberate steps to disclose the algorithm in a public forum soon after it was invented. More than a year passed after this public disclosure and the authors deliberately took no steps to patent the FNV algorithm. Therefore it is safe to say that the FNV authors have no patent claims on the FNV algorithm as published.

A favor - if you use FNV

If you use an FNV function in an application, why not tell tells us about it by sending Email to:

FNV Email addr

Please include the phrase FNV hash function somewhere is the subject line of your Email.

There is no requirement to tell us you are using FNV, however if you do, we will be happy to add your application to the above list.

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The core of the FNV hash

The core of the FNV-1 hash algorithm is as follows: 

hash = offset_basis
for each octet_of_data to be hashed
 hash = hash * FNV_prime
 hash = hash xor octet_of_data
return hash

The offset_basis and FNV_prime can be found in the parameters of the FNV-1/FNV-1a hash section below.

NOTE: We recommend that you use the FNV-1a alternative algorithm instead of the FNV-1 hash where possible.

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FNV-1a alternate algorithm

There is a minor variation of the FNV hash algorithm known as FNV-1a: 

hash = offset_basis
for each octet_of_data to be hashed
 hash = hash xor octet_of_data
 hash = hash * FNV_prime
return hash

The only difference between the FNV-1a hash and the FNV-1 hash is the order of the xor and multiply. The FNV-1a hash uses the same FNV_prime and offset_basis as the FNV-1 hash of the same n-bit size.

The offset_basis and FNV_prime can be found in the parameters of the FNV-1/FNV-1a hash section below.

Some people use FNV-1a instead of FNV-1 because they see slightly better dispersion for tiny (<4 octets) chunks of memory.

One person reported that the FNV-1 hash was not as good as the FNV-1a hash, for their purposes, because the final octet is not as well dispersed. They reported that the FNV-1a hash was better for error detection, for example.

Other people report that either FNV-1 or FNV-1a make a fine hash. (Try it with with just a dash of Sage and ground Cloves :-))

NOTE: We recommend that you use the FNV-1a alternative algorithm instead of the FNV-1 hash where possible.

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Parameters of the FNV-1/FNV-1a hash

The FNV-1 hash parameters are as follows:

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A few remarks on FNV primes

While theory behind FNV_prime's is beyond the scope of this web page, the following text may suffice to satisfy the curious:

One of the key properties to look for in an FNV_prime is how it impacts dispersion.

When s is an integer and 4 < s < 11, then FNV_prime is the smallest prime p of the form:

256int((5 + 2s)/12) + 28 + b
such that:

An FNV_prime that matches the above constraints tend to have better dispersion properties. They improve the polynomial feedback characteristic when an FNV_prime multiplies an intermediate hash value. The hash values produced are more scattered throughout the n-bit hash space.

It is a nice side effect that FNV_prime may be optimized by some compilers for some hardware. On some hardware, replacing the FNV_prime multiply with a set of shifts and adds will improve performance. In other cases where multiply may be pipelined (such as in vector mode), the set of shifts and adds may be sub-optimal. The FNV_prime were not selected for compiler optimization, they were selected for the quality of resulting hash function.

In the case where s = 5, both 16777499 and 16777619 could have been used. The narrowness of the 32-bit hash suggested that the larger prime might be better. It turned out that this level of caution was not warranted. When larger FNV hashes were developed, we opted to select the smallest prime. For compatibility with the original IEEE POSIX P1003.2 committee proposal, the historic FNV_prime for the s = 5 case was kept. The requirement that the FNV_prime mod 240 - 224 - 1 (1099494850559) must be > 224 + 28 + 27 (16777600) was added to harmonize the FNV_primes across 4 < s < 11.

The case where s < 5 is not considered because the resulting hash quality is too low. Such small hashes can, if desired, be derived from a 32 bit FNV hash by xor-folding.

The case where s > 10 is considered because the doubtful utility of such large FNV hashes and because the criteria for such large FNV_Primes is more complex, due to the sparsity of such large primes, and would needlessly clutter the criteria given above. The criteria above is a simplified form that fails to generate 2048-bit FNV_prime and a 4096-bit FNV_prime, for example. For such large primes we would need to use a more extensive prime selection criteria.

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Changing the FNV hash size - xor-folding

If you need an x-bit hash where x is not a power of 2, then we recommend that you compute the FNV hash that is just larger than x-bits and xor-fold the result down to x-bits. By xor-folding we mean shift the excess high order bits down and xor them with the lower x-bits.

For example to produce a 24 bit FNV-1 hash in C we xor-fold fold a 32 bit FNV-1 hash: 

#define MASK_24 (((u_int32_t)1<<24)-1) /* i.e., (u_int32_t)0xffffff */
#define FNV1_32_INIT ((u_int32_t)2166136261)
u_int32_t hash;
void *data;
size_t data_len;

hash = fnv_32_buf(data, data_len, FNV1_32_INIT);
hash = (hash>>24) ^ (hash & MASK_24);

To produce a 16 bit FNV-1 hash in C we xor-fold fold a 32 bit FNV-1 hash: 

#define MASK_16 (((u_int32_t)1<<16)-1) /* i.e., (u_int32_t)0xffff */
#define FNV1_32_INIT ((u_int32_t)2166136261)
u_int32_t hash;
void *data;
size_t data_len;

hash = fnv_32_buf(data, data_len, FNV1_32_INIT);
hash = (hash>>16) ^ (hash & MASK_16);

To produce a 56 bit FNV-1 hash in C (on a machine with 64 bit unsigned values) we xor-fold fold a 64 bit FNV-1 hash: 

#define MASK_56 (((u_int64_t)1<<56)-1) /* i.e., (u_int64_t)0xffffffffffffff */
#define FNV1_64_INIT ((u_int64_t)14695981039346656037)
u_int64_t hash;
void *data;
size_t data_len;

hash = fnv_64_buf(data, data_len, FNV1_64_INIT);
hash = (hash>>56) ^ (hash & MASK_56);

The above process assumes that you are using an FNV hash that at most twice as large as the x-bits that you need. For x < 16, there is no 16 bit (or less) FNV-1 hash to use.

For tiny x < 16 bit values, we recommend using a 32 bit FNV-1 hash as follows: 

/* NOTE: for 0 < x < 16 ONLY!!! */
#define TINY_MASK(x) (((u_int32_t)1<<(x))-1)
#define FNV1_32_INIT ((u_int32_t)2166136261)
u_int32_t hash;
void *data;
size_t data_len;

hash = fnv_32_buf(data, data_len, FNV1_32_INIT);
hash = (((hash>>x) ^ hash) & TINY_MASK(x));

At the expense of CPU performance, one may use a larger FNV-1 hash that is normally required in any of the above xor-folding examples. This will not produce the same standard output, but it may provide slightly better dispersion at the expense of more CPU time. All that is needed is to use a larger FNV-1 hash and to move the mask outside of the expression on the final statement.

For example, to produce a 24 bit FNV-1 hash could have used a 64 bit FNV-1 hash, in a non-standard way, as follows: 

/* NOTE: non-standard use of a larger hash */
#define MASK_24 (((u_int64_t)1<<24)-1) /* i.e., (u_int64_t)0xffffff */
#define FNV1_64_INIT ((u_int64_t)14695981039346656037)
u_int64_t hash;
void *data;
size_t data_len;

hash = fnv_64_buf(data, data_len, FNV1_64_INIT);
hash = (((hash>>24) ^ hash) & MASK_24);

Replacing a 32 bit FNV-1 hash with a 64 bit FNV-1 hash during xor-folding might yield better dispersion at the expense of CPU time. However using an even larger FNV-1 hash is almost certainly a waste of CPU time. If you are going to use this non-standard xor-folding method, we recommend that you only do it for x < 32 bits, and only replace the 32 bit FNV-1 hash with a 64 bit FNV-1 hash.

NOTE: One may substitute the FNV-1a hash for the FNV-1 hash in any of the xor-folding examples. Some people believe that FNV-1a xor-folding gives then slightly better dispersion without any impact on CPU performance. See the FNV-1a hash description for more information.

If you really need an x-bit hash for x > 1024 bits, send us Email.

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Changing the FNV hash size - non-powers of 2

The FNV hash is designed for hash sizes that are a power of 2. If you need a hash size that is not a power of two, then you have two choices. One method id called the lazy mod mapping method and the other is called the retry method. Both involve mapping a range that is a power of 2 onto an arbitrary range.

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FNV source

FNV reference source

In the C source< below, primes are provided for 32 bit and 64 bit unsigned integers. For compilers that do not implement the unsigned long long type, code is provided to quickly simulate the 64 bit multiply by the particular FNV_prime.

NOTE: As of version 5.0, the above source include test vectors for 32 bit and 64 bit versions of the FNV-0, FNV-1, and FNV-1a algorithms. The test_fnv.c file contains validated test vectors. To verify a compiled code, try:
make check
For compiled code, try:
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Other FNV source code

Andy Allinger sent us this 32 bit FNV-1a subroutine written in FNV-1 in FORTRAN.

Nicola Bonelli has an implementation of FNV using the iovec interface:

Nicola Bonelli also wrote the following C++ FNV implementation:

Georgi Marinov (Georgi 'Kaze' 'Sanmayce') posted his very fast FNV-1a implementation:

Wayne Diamond implemented 32-bit FNV algorithm in PowerBASIC inline x86 assembly: 


FUNCTION FNV32(BYVAL dwOffset AS DWORD, BYVAL dwLen AS DWORD, BYVAL offset_basis AS DWORD) AS DWORD
#REGISTER NONE
! mov esi, dwOffset ;esi = ptr to buffer
! mov ecx, dwLen ;ecx = length of buffer (counter)
! mov eax, offset_basis ;set to 2166136261 for FNV-1
! mov edi, &h01000193 ;FNV_32_PRIME = 16777619
! xor ebx, ebx ;ebx = 0
nextbyte:
! mul edi ;eax = eax * FNV_32_PRIME
! mov bl, [esi] ;bl = byte from esi
! xor eax, ebx ;al = al xor bl
! inc esi ;esi = esi + 1 (buffer pos)
! dec ecx ;ecx = ecx - 1 (counter)
! jnz nextbyte ;if ecx is 0, jmp to NextByte
! mov FUNCTION, eax ;else, function = eax
END FUNCTION

Wayne said:

''Just thought I should let you know that I've ported the 32-bit FNV algorithm over to inline assembly. It's actually in PowerBASIC (www.powerbasic.com) format - a compiler I use, but the main function is all assembly. It could be optimized further in terms of saving a couple of clock cycles, but it's fairly optimized al ready - only 6 instructions in the main loop, plus 5 setup instructions, and compiles to just 33 bytes.''

M.S.Schulte sent us these 32-bit FNV-1 and FNV-1a x86 assembler implementations (written in flat assembler), half of which were optimized for speed, the other half were optimized for size: 


small_fnv32: ;FNV1 32bit (size: 31 bytes)
; Intel Core 2 Duo E6600: 354.20 mb/s
   push esi
   push edi
   mov esi, [esp + 0ch] ;buffer
   mov ecx, [esp + 10h] ;length
   mov eax, [esp + 14h] ;basis
   mov edi, 01000193h ;fnv_32_prime
 next:
   mul edi
   xor al, [esi]
   inc esi
   loop snext
   pop edi
   pop esi
   retn 0ch

 small_fnv32a: ;FNV1a 32bit (size: 31 bytes)
; Intel Core 2 Duo E6600: 327.68 mb/s
   push esi
   push edi
   mov esi, [esp + 0ch] ;buffer
   mov ecx, [esp + 10h] ;length
   mov eax, [esp + 14h] ;basis
   mov edi, 01000193h ;fnv_32_prime
 nexta:
   xor al, [esi]
   mul edi
   inc esi
   loop nexta
   pop edi
   pop esi
   retn 0ch

fast_fnv32: ;FNV1 32bit (size: 36 bytes)
; Intel Core 2 Duo E6600: 565.12 mb/s
   push ebx
   push esi
   push edi
   mov esi, [esp + 10h] ;buffer
   mov ecx, [esp + 14h] ;length
   mov eax, [esp + 18h] ;basis
   mov edi, 01000193h ;fnv_32_prime
   xor ebx, ebx
 next:
   mul edi
   mov bl, [esi]
   xor eax, ebx
   inc esi
   dec ecx
   jnz next
   pop edi
   pop esi
   pop ebx
   retn 0ch

 fast_fnv32a: ;FNV1a 32bit (size: 36 bytes)
; Intel Core 2 Duo E6600: 574.95 mb/s
   push ebx
   push esi
   push edi
   mov esi, [esp + 10h] ;buffer
   mov ecx, [esp + 14h] ;length
   mov eax, [esp + 18h] ;basis
   mov edi, 01000193h ;fnv_32_prime
   xor ebx, ebx
 nexta:
   mov bl, [esi]
   xor eax, ebx
   mul edi
   inc esi
   dec ecx
   jnz nexta
   pop edi
   pop esi
   pop ebx
   retn 0ch

M.S.Schulte also sent us these 64-bit FNV-1 and FNV-1a x86 assembler implementations: 


;FNV64 x86-64bit assembler implementation (written in flat assembler)
;FNV64-1 and FNV64-1a, both 37 bytes, (~284.13 mb/s Intel E8400)
;invoke fnv64,buffer,length,base (x64 Calling Convention)

  fnv64:
    mov rax, r8
    mov r8, rdx
    mov r9, 100000001b3h ;fnv_64_prime
    xor r10, r10
  next:
    mul r9
    mov r10b, [rcx]
    xor rax, r10
    inc rcx
    dec r8
    jnz next
    ret

  fnv64a:
    mov rax, r8
    mov r8, rdx
    mov r9, 100000001b3h ;fnv_64_prime
    xor r10, r10
  nexta:
    mov r10b, [rcx]
    xor rax, r10
    mul r9
    inc rcx
    dec r8
    jnz nexta
    ret

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gcc optimization

It has been reported by several people that under the gcc compiler with -O3 on many AMD & Intel CPUs, that replacing the FNV_prime multiply with a expression of shifts and adds will improve the performance.

Limited testing on our part confirmed that one can gain a few % in speed on an 1.6GHz AMD Athlon using gcc version 3.2.2 with -O3 optimization.

For a 32 bit FNV-1, we used: 

while (bp < be) {

    /* multiply by the 32 bit FNV magic prime mod 2^32 */
#if defined(NO_FNV_GCC_OPTIMIZATION)
    hval *= FNV_32_PRIME;
#else
    hval += (hval<<1) + (hval<<4) + (hval<<7) + (hval<<8) + (hval<<24);
#endif

    /* xor the bottom with the current octet */
    hval ^= (uint32_t)(*bp++);
}

For a 32 bit FNV-1a, we used: 

while (bp < be) {

    /* xor the bottom with the current octet */
    hval ^= (uint32_t)(*bp++);

    /* multiply by the 32 bit FNV magic prime mod 2^32 */
#if defined(NO_FNV_GCC_OPTIMIZATION)
    hval *= FNV_32_PRIME;
#else
    hval += (hval<<1) + (hval<<4) + (hval<<7) + (hval<<8) + (hval<<24);
#endif
}

For a 64 bit FNV-1, we used: 

while (bp < be) {

    /* multiply by the 64 bit FNV magic prime mod 2^64 */
#if defined(NO_FNV_GCC_OPTIMIZATION)
    hval *= FNV_64_PRIME;
#else
    hval += (hval << 1) + (hval << 4) + (hval << 5) +
     (hval << 7) + (hval << 8) + (hval << 40);
#endif

    /* xor the bottom with the current octet */
    hval ^= (uint64_t)(*bp++);
}

For a 64 bit FNV-1a, we used: 

while (bp < be) {

    /* xor the bottom with the current octet */
    hval ^= (uint64_t)(*bp++);

    /* multiply by the 64 bit FNV magic prime mod 2^64 */
#if defined(NO_FNV_GCC_OPTIMIZATION)
    hval *= FNV_64_PRIME;
#else
    hval += (hval << 1) + (hval << 4) + (hval << 5) +
     (hval << 7) + (hval << 8) + (hval << 40);
#endif
}

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Can you help solve some of the zero-hash challenges?

We are interested in finding the shortest data sets, under certain constraints, that produce a FNV hash value of zero for the various sizes of the FNV-1 and FNV-1a hash function. Those who offer the best solution will receive fame and credit on the FNV web page.

If you have a zero-value hash solution to an unsolved challenge, or if you have a better (shorted data segment) solution than one that is shown below, please send Email to:

FNV Email addr

Please use the subject line: 

zero-hash challenge solution

NOTE: Please use the solution format used by Russ Cox (see below), if possible.

Please include the following information in your Email message:

  1. The challenge number you claim to have solved
  2. The name of the challenge you claim to have solved
  3. The length, in octets (8 bit bytes) of your proposed solution
  4. Who should we credit (i.e., how do you want us to credit you on our web page) for solving the challenge?
  5. A URL containing your proposed solution (optional)
NOTE: If your solution is large, please do not send the data set in the Email. Instead send is a URL where we can download your proposed challenge solution.
Zero-hash challenges:
  1. SOLVED! What is the shortest binary data set for which the 32-bit FNV-1 hash is 0?
    32-bit solution by Russ Cox <rcs Email address> on 2011-Mar-02: 
    There are 254 solutions of length 5, ranging from

FNV32_1(01 47 6c 10 f3) = 0

to

FNV32_1(fd 45 41 08 a0) = 0

  2. SOLVED! What is the shortest binary data set for which the 64-bit FNV-1 hash is 0?
    Scott Pakin <pakin Email address> on 2011-Aug-22 reported that there are no solutions for binary data sets of length 7 or less.

    64-bit solution by an anonymous scientist <ntldr Email address> on 2011-Oct-23: 

    There are no solutions for length 8.

These are the solutions for length 9:

FNV64_1(92 06 77 4c e0 2f 89 2a d2) = 0
FNV64_1(fb 6c 4f db 00 41 db c0 fe) = 0
FNV64_1(9f 72 72 35 80 4b 8d 6b 06) = 0
FNV64_1(3d 82 76 00 80 7c 52 62 1a) = 0
FNV64_1(58 21 f5 a2 e1 01 9d 80 e0) = 0
FNV64_1(52 a1 eb 10 a0 e9 45 96 05) = 0
FNV64_1(be 64 8a 14 e1 46 17 18 ff) = 0
FNV64_1(9e 50 1d f2 41 75 55 ac 05) = 0
FNV64_1(b3 92 a9 6f 80 e4 29 a4 63) = 0
FNV64_1(82 ba b3 41 81 0f db 83 15) = 0
FNV64_1(92 f4 6e 0e e1 b9 e5 45 2d) = 0
FNV64_1(3c ea 57 50 81 67 67 9b e0) = 0
FNV64_1(36 e3 96 34 e2 1d 36 00 61) = 0
FNV64_1(af fa ff ee 61 b0 5e c4 04) = 0
FNV64_1(d5 c9 88 15 02 2f d3 38 c2) = 0
FNV64_1(bc a7 38 51 e2 2f b1 1b 22) = 0
FNV64_1(70 f2 10 ba 02 45 37 b3 e8) = 0
FNV64_1(5b a3 a0 4e 81 fc 4f 32 5b) = 0
FNV64_1(cd 50 99 68 22 d4 78 2f b0) = 0
FNV64_1(fa ff 0d fa e2 f0 43 b4 9a) = 0
FNV64_1(16 3f ba 47 43 94 44 fe 86) = 0
FNV64_1(46 e0 03 71 c2 57 f0 bc da) = 0
FNV64_1(60 74 4a 52 e3 06 42 36 f2) = 0
FNV64_1(97 20 3a f8 a2 f6 8a 62 a6) = 0
FNV64_1(98 f5 cc d5 03 32 22 1a e2) = 0
FNV64_1(5d d5 14 e8 e3 43 8b 5a 9e) = 0
FNV64_1(95 b8 11 62 03 5a ed d2 cb) = 0
FNV64_1(f9 cb 23 1d 03 71 c5 ca 5c) = 0
FNV64_1(c3 04 1c 59 82 a5 aa 9b 55) = 0
FNV64_1(68 10 80 61 a3 5e 72 31 48) = 0
FNV64_1(43 0a eb 89 c2 c1 9d d8 2a) = 0
FNV64_1(5a a3 e3 40 23 ce 90 bc a2) = 0
FNV64_1(27 e1 3f aa a3 8f af 6a 51) = 0
FNV64_1(0c 5b ac 36 24 22 a2 7c 24) = 0
FNV64_1(ea bc d7 7c 24 49 58 66 57) = 0
FNV64_1(5a 30 62 51 83 9c 97 c3 75) = 0
FNV64_1(7a 18 75 d3 c3 88 65 0b 3a) = 0
FNV64_1(02 38 25 95 25 0b 3b 0c a8) = 0
FNV64_1(33 1c ae dd 83 fc 55 f4 63) = 0
FNV64_1(cb 87 3d b9 e5 38 0b bd ca) = 0
FNV64_1(3a 25 ba 67 a4 c7 49 80 e9) = 0
FNV64_1(49 14 3b 94 05 63 b5 de d6) = 0
FNV64_1(45 fb 0d 28 45 19 66 63 27) = 0
FNV64_1(92 7a e5 a6 e5 88 ba 55 68) = 0
FNV64_1(c3 93 7c 11 c4 1a 2f e0 8b) = 0
FNV64_1(a1 d8 5e 71 a5 6a 96 5e 64) = 0
FNV64_1(77 7b d7 7d 05 dc 73 64 c3) = 0
FNV64_1(3d 3f d4 d6 a6 71 b2 9d 65) = 0
FNV64_1(8d 45 9e d0 27 66 b4 46 34) = 0
FNV64_1(f1 da 16 a1 85 fe 43 a7 30) = 0
FNV64_1(97 6b 02 e3 66 10 3d 6e ab) = 0
FNV64_1(84 2b d9 13 a7 25 5a 8a 22) = 0
FNV64_1(0c 2b 2f d2 28 3a 91 df 95) = 0
FNV64_1(1c 01 ed aa 47 2f 64 6a 8b) = 0
FNV64_1(71 66 6f 98 47 74 48 eb 39) = 0
FNV64_1(2b b3 61 de e8 6c 33 fd 32) = 0
FNV64_1(c5 33 7e c3 87 9c 0c 24 4b) = 0
FNV64_1(b7 44 ea 2c a8 59 bc fc c5) = 0
FNV64_1(b2 8c 40 98 67 46 6f ce 35) = 0
FNV64_1(04 34 61 b3 87 d4 e5 1a 7f) = 0
FNV64_1(20 ba 15 17 e8 dd d9 f6 19) = 0
FNV64_1(36 c4 d3 ef 88 53 6e 86 56) = 0
FNV64_1(32 55 ce f0 48 73 af 8d 9d) = 0
FNV64_1(18 3c d8 70 08 71 6a 47 a3) = 0
FNV64_1(a8 ad fb 29 a8 e4 8e 82 c4) = 0
FNV64_1(47 47 bf 58 08 7f ab bc 34) = 0
FNV64_1(8f 68 71 3a e9 56 8f d0 0f) = 0
FNV64_1(64 5e dc 14 88 93 8d b4 35) = 0
FNV64_1(b4 33 d0 6d 48 bb 3a 5d 3d) = 0
FNV64_1(22 e4 4d 0a 48 bd 95 1e 8e) = 0
FNV64_1(78 6e 06 7d 48 ce db 12 33) = 0
FNV64_1(7e 1f 4d 02 48 f8 d2 a5 c2) = 0
FNV64_1(90 6b 26 4e c7 ef 12 f2 20) = 0
FNV64_1(90 10 a8 21 09 16 22 57 bc) = 0
FNV64_1(5b 1a 8c bc 09 2c a4 2d 9c) = 0
FNV64_1(2c 1a 6e 44 a9 7d 98 e0 39) = 0
FNV64_1(8a 2b 35 ab 49 97 d5 f7 bc) = 0
FNV64_1(29 bc 62 5e 0a 4e 9e 34 40) = 0
FNV64_1(e7 e6 c7 00 aa d3 26 5a 4a) = 0
FNV64_1(7e 65 e5 51 2b 66 e8 b5 b2) = 0
FNV64_1(2b d7 cf 6a 6a 6f b4 56 c9) = 0
FNV64_1(33 51 09 af ab 42 80 8b 07) = 0
FNV64_1(d1 78 30 6b c9 9c af 1f d4) = 0
FNV64_1(c6 00 f9 bf 4b 38 f0 00 c6) = 0
FNV64_1(a1 81 99 9a c9 f2 8e 4c 6f) = 0
FNV64_1(b3 d1 6c 57 2c 62 3c b0 5c) = 0
FNV64_1(c7 50 c1 4d ec de 91 e8 fd) = 0
FNV64_1(54 51 fe aa ec e9 6b f2 a2) = 0
FNV64_1(5d dc 27 f3 4b c8 b0 9a c9) = 0
FNV64_1(d2 4d e1 77 8c 0a 8f 2d 44) = 0
FNV64_1(ce e4 e5 80 ca 8a 07 dc 67) = 0
FNV64_1(0f d0 8f 67 ca 9f 94 a5 86) = 0
FNV64_1(89 e9 ed dd ed 84 84 50 26) = 0
FNV64_1(76 f5 be 03 ac 82 5a 09 26) = 0
FNV64_1(f8 71 02 ca 6c 6d a5 ae fc) = 0
FNV64_1(e8 cb 80 56 ad 00 a0 d1 d2) = 0
FNV64_1(88 89 0c dd 0c cf b2 5d d7) = 0
FNV64_1(69 ad 8f db 0d 03 8a ca 37) = 0
FNV64_1(96 58 24 93 cb bf d7 f1 fe) = 0
FNV64_1(ee b1 f6 d2 6d 9b 46 7d 3f) = 0
FNV64_1(de 64 18 d6 2e 86 5b 3c 0c) = 0
FNV64_1(24 05 66 e4 0d f1 c8 b1 d3) = 0
FNV64_1(77 d7 5f 5f ef 81 2d b3 37) = 0
FNV64_1(58 53 f5 b5 2e ec 51 fe 25) = 0
FNV64_1(ba 65 2a 3b 8e c6 bb a8 b6) = 0
FNV64_1(e5 81 4f 09 f0 0c ec f9 fa) = 0
FNV64_1(50 5b e8 f9 f0 6a 47 b4 64) = 0
FNV64_1(d3 0e f4 c7 6e d9 60 31 b5) = 0
FNV64_1(58 e4 4a 3c cd 97 d6 fd 84) = 0
FNV64_1(6f 82 aa ca 2f e7 1a 8d b1) = 0
FNV64_1(8f 50 ec 2f 2f e7 30 4c db) = 0
FNV64_1(f0 3b 01 db 6f 33 db 82 41) = 0
FNV64_1(13 3c 71 e4 8f 75 46 48 8f) = 0
FNV64_1(2f a5 a5 41 cd f5 b4 c6 45) = 0
FNV64_1(8b 1a 4c 12 30 38 c3 61 08) = 0
FNV64_1(6f 9c 5c 3f 8f d6 47 70 f7) = 0
FNV64_1(c1 0e 16 18 50 1b 47 48 f8) = 0
FNV64_1(2b 94 3f ad 30 ad 5e c4 85) = 0
FNV64_1(5f 55 92 c6 ce b9 f5 05 08) = 0
FNV64_1(42 8e 3a bb f1 bd 08 09 25) = 0
FNV64_1(28 84 f5 2b ce f1 3e 47 41) = 0
FNV64_1(25 d1 2c bf 90 5c 71 24 85) = 0
FNV64_1(d0 25 3d f3 90 64 67 ae f9) = 0
FNV64_1(c5 1d e5 36 11 a9 7b 4d e0) = 0
FNV64_1(88 c2 24 da 50 f9 55 03 dc) = 0
FNV64_1(ff 54 4f 75 cf 6d bb c4 4b) = 0
FNV64_1(9e 49 c2 63 11 d7 b0 74 25) = 0
FNV64_1(ac b1 42 65 cf 7d 84 0e 37) = 0
FNV64_1(05 a5 28 18 11 e3 0d 6a aa) = 0
FNV64_1(03 8d 11 ce f2 6f 0e 0a cf) = 0
FNV64_1(bf d6 88 3d 51 75 18 67 0e) = 0
FNV64_1(69 a2 dd 69 cf e4 94 5e e3) = 0
FNV64_1(e4 62 0b 95 b1 58 a1 d4 25) = 0
FNV64_1(c0 75 c6 ec 51 9e d4 c7 4c) = 0
FNV64_1(83 9d b3 97 32 54 9b 04 ec) = 0
FNV64_1(9a 7f 71 94 32 cf bb 97 38) = 0
FNV64_1(7a 4f e4 60 13 93 fd 7d 50) = 0
FNV64_1(76 48 71 f5 52 2f cb f7 e2) = 0
FNV64_1(da 0e 88 1f 13 ba d5 a7 2f) = 0
FNV64_1(2a be ca e7 33 12 4e 33 26) = 0
FNV64_1(79 ce 5e ee 92 27 5d c7 17) = 0
FNV64_1(36 91 77 d3 72 5a de 9f 0b) = 0
FNV64_1(3a 33 cd 8d 52 7a b8 2a d8) = 0
FNV64_1(25 66 ec c3 52 8b d0 13 4f) = 0
FNV64_1(de d7 a1 1f b2 58 65 d8 d7) = 0
FNV64_1(8a e5 cb 54 33 b0 de 92 42) = 0
FNV64_1(71 49 0a bb 33 d8 35 b3 59) = 0
FNV64_1(03 36 3b 64 f4 98 4b 21 99) = 0
FNV64_1(8c f5 50 02 d2 10 db 86 1d) = 0
FNV64_1(c3 4f cf 6e 93 4e b5 d8 b4) = 0
FNV64_1(2a fb 95 75 73 8c 85 76 82) = 0
FNV64_1(35 c0 2a 8b f5 56 45 66 45) = 0
FNV64_1(68 2a 76 44 73 cf 31 3a 8e) = 0
FNV64_1(98 4c a0 05 93 9a cf 65 a1) = 0
FNV64_1(a5 3e 3b f8 94 0e 6e 74 73) = 0
FNV64_1(4b 75 16 e9 35 47 e2 af 21) = 0
FNV64_1(3c 84 fb ee f6 10 6c 09 3f) = 0
FNV64_1(45 52 87 53 74 7c 1b 2c a1) = 0
FNV64_1(a0 8b 28 e0 d3 34 be 90 cb) = 0
FNV64_1(67 57 50 d0 16 3c 23 af e1) = 0
FNV64_1(a8 a6 4d 44 16 52 57 ba 95) = 0
FNV64_1(9e 0c be 6a 75 1d 3f 6c 20) = 0
FNV64_1(14 1b 43 7a b5 4e 40 88 b0) = 0
FNV64_1(68 3b bd d6 f7 ae d7 f9 28) = 0
FNV64_1(ab c0 61 a3 76 20 b8 f7 3b) = 0
FNV64_1(05 e8 00 91 b5 dd be 7e af) = 0
FNV64_1(14 dd 60 a4 96 19 04 05 16) = 0
FNV64_1(7e e5 14 cd 76 87 03 4c 2d) = 0
FNV64_1(07 f0 09 29 18 7d 7d fe 8a) = 0
FNV64_1(b9 b4 a5 c6 37 99 fd 49 ff) = 0
FNV64_1(d2 dd 5a 63 37 e4 08 8e d4) = 0
FNV64_1(a2 0b f2 5e 76 fd 65 2c 80) = 0
FNV64_1(c8 d7 df ba 37 e8 d9 2b 0c) = 0
FNV64_1(6e 40 03 eb 37 ea eb a6 93) = 0
FNV64_1(27 f9 53 0f 37 fc 0e 28 60) = 0
FNV64_1(c2 72 49 23 d5 ce 7e bb ef) = 0
FNV64_1(3e 11 d8 6b b6 e9 30 2f ab) = 0
FNV64_1(0e dd b7 d7 19 45 86 d7 79) = 0
FNV64_1(a3 f7 21 85 97 07 7d e1 4b) = 0
FNV64_1(4e 76 21 ee 19 67 54 55 23) = 0
FNV64_1(0f 19 18 da 38 60 1c 0b 9c) = 0
FNV64_1(a4 91 5d 2c 77 7f b4 cb c6) = 0
FNV64_1(c1 b7 ee 41 19 7a 60 4d 7e) = 0
FNV64_1(88 47 7b 0c d6 4c e0 c1 20) = 0
FNV64_1(73 88 eb 4f d6 53 4f 7c 6a) = 0
FNV64_1(f4 5a e5 b3 f9 cf 96 88 8f) = 0
FNV64_1(ba 5c b1 28 58 2f 33 16 cc) = 0
FNV64_1(04 cd 1f c8 1a 7a 20 f1 d0) = 0
FNV64_1(5f 2c 1c 63 b8 48 83 82 a4) = 0
FNV64_1(22 f5 ed a6 98 51 eb a3 f8) = 0
FNV64_1(f8 6b 6d 33 fa 65 24 bd 5c) = 0
FNV64_1(10 3b b6 ae d7 86 73 25 d3) = 0
FNV64_1(52 31 6c 5a 79 03 be 55 95) = 0
FNV64_1(af c9 ab 5e 1b 54 de 1d 84) = 0
FNV64_1(c2 ed f4 36 79 77 81 0d ee) = 0
FNV64_1(36 f5 db eb d8 30 d9 69 f6) = 0
FNV64_1(43 84 92 b9 79 90 66 a4 e6) = 0
FNV64_1(7d e9 4d 0e 1b da 69 eb 57) = 0
FNV64_1(2d 03 20 62 fb 3b 6e 88 65) = 0
FNV64_1(e5 69 ec d2 79 be d8 aa 8e) = 0
FNV64_1(ac 26 0a dd fb 68 43 1f 6d) = 0
FNV64_1(3c 96 c1 be 3a be 22 ae 76) = 0
FNV64_1(de 73 09 f1 1c 39 67 8a 0c) = 0
FNV64_1(56 2e 5f 2c 3a fd 30 40 7d) = 0
FNV64_1(68 57 ce 1c 59 e0 e0 eb 04) = 0
FNV64_1(df f7 e6 75 1c 66 88 86 90) = 0
FNV64_1(fd af f5 8b 5a 06 ae 0b 40) = 0
FNV64_1(4e cf a7 e9 1c 93 af 36 a8) = 0
FNV64_1(56 dc 13 cf fc 12 88 bb b8) = 0
FNV64_1(1f 5f c2 b2 3b 75 fb 7c 92) = 0
FNV64_1(4e 9c bb ba 5a 74 e3 a4 e1) = 0
FNV64_1(0b a0 c8 c5 1d 99 06 87 5e) = 0
FNV64_1(ff ef b0 25 1d f4 9d df db) = 0
FNV64_1(09 67 cb 8f 7c 13 3c 75 97) = 0
FNV64_1(05 bf fe 4d fd d2 6e 61 64) = 0
FNV64_1(a4 d7 4b 6d 3d 2a bb ee 4c) = 0
FNV64_1(b9 8c 01 cb 5b f2 50 15 f0) = 0
FNV64_1(31 45 17 91 1e a3 7f 25 52) = 0
FNV64_1(10 6c 0c 98 db 0f 9b 1e 88) = 0
FNV64_1(06 ec cc b6 9b da a2 3a 16) = 0
FNV64_1(23 66 38 19 7c ac 80 d3 78) = 0
FNV64_1(b8 f3 d7 98 bc 11 60 0f bf) = 0
FNV64_1(27 24 2d a8 db c2 99 28 65) = 0
FNV64_1(64 61 39 c2 bc 79 b5 b1 a6) = 0
FNV64_1(df ff 2a 12 5c fb 42 6d 01) = 0
FNV64_1(af 1d ea 4e ff 0d 46 95 5e) = 0
FNV64_1(2a b0 c6 54 9c e9 98 43 e1) = 0
FNV64_1(7c e5 9e 74 7d c8 44 ef 9e) = 0
FNV64_1(56 14 d1 31 dc ce 77 17 c3) = 0
FNV64_1(ed 6b 65 68 3f 05 36 41 9b) = 0
FNV64_1(2f d2 24 7e dd 19 4f 91 72) = 0
FNV64_1(c8 96 f0 54 9d 92 5b cc b1) = 0
FNV64_1(47 5d 76 63 be 17 24 ad d4) = 0
FNV64_1(4f 88 0b 03 9e 4a 48 ee 14) = 0
FNV64_1(26 ec 1b 56 5e b8 5d 5e 39) = 0
FNV64_1(c3 a8 2d 1a 5e fc b7 81 49) = 0
FNV64_1(14 3a 3b 0b be e7 b2 4d 75) = 0
FNV64_1(27 a0 f4 22 df b5 b6 5e 4a) = 0

  3. Partial solution: What is the shortest binary data set for which the 128-bit FNV-1 hash is 0?

    Richard Heylen <richard_in_reading Email address> found a 128-bit FNV-1 solution on 2011-Dec-01: 
    The following is a solution of length 17:

FNV128_1(20 28 4e 43 40 55 6f 99 25 1b 89 f4 a8 18 ec 76 c0) = 0
    NOTE: It is not known if the above solution is the shortest 128-bit FNV-1 solution.

    Can you find a shorter solution or prove that the shortest solutions are of length 17?

  4. Partial solution: What is the shortest binary data set for which the 256-bit FNV-1 hash is 0?

    Richard Heylen <richard_in_reading Email address> found a 256-bit FNV-1 solution on 2011-Dec-17: 
    The following is a solution of length 37:

FNV256_1(04 03 F4 7D 37 15 6D DB 3B 06 68 6F 07 0E 0E 3B 67 6E 43 53 0B
    
5F 5A 08 93 09 16 29 47 D9 4C 1B BD 7E 04 17 38) = 0
    NOTE: It is not known if the above solution is the shortest 256-bit FNV-1 solution.

    Richard Heylen speculates that the shortest solution might be 32 or 33 in length.

    Can you find a shorter solution or prove that the shortest solutions are of length 37?

  5. What is the shortest binary data set for which the 512-bit FNV-1 hash is 0?

  6. What is the shortest binary data set for which the 1024-bit FNV-1 hash is 0?

  7. SOLVED! What is the shortest binary data set for which the 32-bit FNV-1a hash is 0?
    32-bit solution by Russ Cox <rcs Email address> on 2011-Mar-02: 
    The solutions of length 4 are:

FNV32_1a(cc 24 31 c4) = 0
FNV32_1a(e0 4d 9f cb) = 0

  8. SOLVED! What is the shortest binary data set for which the 64-bit FNV-1a hash is 0?
    Scott Pakin <pakin Email address> on 2011-Aug-22 reported that there are no solutions for binary data sets of length 7 or smaller.

    64-bit solution by an anonymous scientist <ntldr Email address> on 2011-Oct-23: 

    The only solution for length 8 is:

FNV64_1a(d5 6b b9 53 42 87 08 36) = 0

  9. What is the shortest binary data set for which the 128-bit FNV-1a hash is 0?

  10. What is the shortest binary data set for which the 256-bit FNV-1a hash is 0?

  11. What is the shortest binary data set for which the 512-bit FNV-1a hash is 0?

  12. What is the shortest binary data set for which the 1024-bit FNV-1a hash is 0?

    NOTE: By binary data set we mean any arbitrary collection of bits that is a multiple of 8 bits (1 octet) in length.

  13. SOLVED! What is the shortest set of consecutive NUL octets for which the 32-bit FNV-1 hash is 0?

  14. SOLVED! What is the shortest set of consecutive NUL octets for which the 64-bit FNV-1 hash is 0?

  15. SOLVED! What is the shortest set of consecutive NUL octets for which the 128-bit FNV-1 hash is 0?

  16. SOLVED! What is the shortest set of consecutive NUL octets for which the 256-bit FNV-1 hash is 0?

  17. SOLVED! What is the shortest set of consecutive NUL octets for which the 512-bit FNV-1 hash is 0?

  18. SOLVED! What is the shortest set of consecutive NUL octets for which the 1024-bit FNV-1 hash is 0?

    NOTE: Russ Cox's solution below is for the set of 6 challenges immediately above

    General FNV solution by Russ Cox <rcs Email address> on 2011-Mar-02: 
    There is no such stream of NUL octets.

Xor with an odd byte flips the parity of the hash.
Xor with an even byte leaves it alone, as does multiplying
by any of the (odd) FNV primes. Thus the final hash has
the same parity as the initial offset if and only if there
are an even number of odd bytes in the input. This is
the reason that all the offset bases have the same parity
(odd, it turns out), and it implies that any consecutive
stream of NULs will have an odd (non-zero) hash.

  19. SOLVED! What is the shortest set of consecutive NUL octets for which the 32-bit FNV-1a hash is 0?

  20. SOLVED! What is the shortest set of consecutive NUL octets for which the 64-bit FNV-1a hash is 0?

  21. SOLVED! What is the shortest set of consecutive NUL octets for which the 128-bit FNV-1a hash is 0?

  22. SOLVED! What is the shortest set of consecutive NUL octets for which the 256-bit FNV-1a hash is 0?

  23. SOLVED! What is the shortest set of consecutive NUL octets for which the 512-bit FNV-1a hash is 0?

  24. SOLVED! What is the shortest set of consecutive NUL octets for which the 1024-bit FNV-1a hash is 0?

    NOTE: Russ Cox's solution below is for the set of 6 challenges immediately above

    General FNV solution by Russ Cox <rcs Email address> on 2011-Mar-02: 
    There is no such stream of NUL octets.

Xor with an odd byte flips the parity of the hash.
Xor with an even byte leaves it alone, as does multiplying
by any of the (odd) FNV primes. Thus the final hash has
the same parity as the initial offset if and only if there
are an even number of odd bytes in the input. This is
the reason that all the offset bases have the same parity
(odd, it turns out), and it implies that any consecutive
stream of NULs will have an odd (non-zero) hash.

    NOTE: By set of consecutive NUL octets we mean consecutive octets of 0 value.

  25. SOLVED! What is the shortest set of consecutive 0xff octets for which the 32-bit FNV-1 hash is 0?
    32-bit solution by Russ Cox <rcs Email address> on 2011-Mar-02: 
    428876705 0xff octets.

    Peter de Rivaz <peter.derivaz Email address> independently confirmed this result.

    Richard Heylen <richard_in_reading Email address> independently confirmed this result.

  26. SOLVED! What is the shortest set of consecutive 0xff octets for which the 64-bit FNV-1 hash is 0?
    64-bit solution by Peter de Rivaz <peter.derivaz Email address> on 2011-Dec-13: 
    9896220416391497057 0xff octets.

    Richard Heylen <richard_in_reading Email address> independently confirmed this result.

  27. SOLVED! What is the shortest set of consecutive 0xff octets for which the 128-bit FNV-1 hash is 0?
    128-bit solution by Richard Heylen <richard_in_reading Email address> on 2011-Dec-14: 
    152812075112152085146780705563019820097 0xff octets.

    Peter de Rivaz <peter.derivaz Email address> independently confirmed this result.

  28. SOLVED! What is the shortest set of consecutive 0xff octets for which the 256-bit FNV-1 hash is 0?
    256-bit solution by Richard Heylen <richard_in_reading Email address> on 2011-Dec-14: 
    971310111339922874984865931636119693708047768520568964839262806324177446
    
08641 0xff octets.

    Peter de Rivaz <peter.derivaz Email address> independently confirmed this result.

  29. SOLVED! What is the shortest set of consecutive 0xff octets for which the 512-bit FNV-1 hash is 0?
    512-bit solution by Richard Heylen <richard_in_reading Email address> on 2011-Dec-14: 
    612806956068056576215461080927099484400241024395026354420378459322301684
    
399722907408508285157251830003265846176457230616192353760639874361657361
    
1559921729 0xff octets.

    Peter de Rivaz <peter.derivaz Email address> independently confirmed this result.

  30. Partial solution: What is the shortest set of consecutive 0xff octets for which the 1024-bit FNV-1 hash is 0?
    Richard Heylen <richard_in_reading Email address> on 2011-Dec-14 found a 1024-bit solution, one that may not be the shortest: 
    416676424643376760772449487657397580462250574503060952762179226758571093
    
761689059455392577969506880247688215845019822014535567311051405867916840
    
497646798425786609620276239990874926250263846724497488057368971095038212
    
934393820920453733216924021449681744199270750560657371464991242494173425
    
0024772314731200245 0xff octets.

    Peter de Rivaz <peter.derivaz Email address> independently confirmed this partial solution.

    NOTE: Russ Cox <rcs Email address> also observed that as a consequence of his solution to the consecutive NUL octet challenge, any consecutive stream of 0xff with a zero FNV-1 or FNV-1a hash of any size must be of odd length.

  31. SOLVED! What is the shortest set of consecutive 0xff octets for which the 32-bit FNV-1a hash is 0?
    32-bit solution by Russ Cox <rcs Email address> on 2011-Mar-02: 
    3039744951 0xff octets.

    Peter de Rivaz <peter.derivaz Email address> independently confirmed this result.

    Richard Heylen <richard_in_reading Email address> independently confirmed this result.

  32. Partial solution: What is the shortest set of consecutive 0xff octets for which the 64-bit FNV-1a hash is 0?
    Peter de Rivaz <peter.derivaz Email address> on 2011-Dec-13 found a 64-bit solution that may not be the shortest: 
    5125902172520635575 0xff octets.

    Richard Heylen <richard_in_reading Email address> independently confirmed this partial solution.

  33. Partial solution: What is the shortest set of consecutive 0xff octets for which the 128-bit FNV-1a hash is 0?
    Peter de Rivaz <peter.derivaz Email address> on 2012-Mar-22 found a 128-bit solution that may not be the shortest: 
    195988526173479582814801599910495893127 0xff octets.

    Richard Heylen <richard_in_reading Email address> independently confirmed this partial solution.

  34. Partial solution: What is the shortest set of consecutive 0xff octets for which the 256-bit FNV-1a hash is 0?
    Peter de Rivaz <peter.derivaz Email address> on 2012-Mar-22 found a 256-bit solution that may not be the shortest: 
    121365261308607922778298441917362349745681574069429011964286973126957522
    
07543 0xff octets.

    Richard Heylen <richard_in_reading Email address> independently confirmed this partial solution.

  35. Partial solution: What is the shortest set of consecutive 0xff octets for which the 512-bit FNV-1a hash is 0?
    Peter de Rivaz <peter.derivaz Email address> on 2012-Mar-22 found a 512-bit solution that may not be the shortest: 
    445359075217293949446034810045247904893303946817563293272717969680141569
    
129699002471949546033702514868111823565737421304575683326671821385410536
    
5691076111 0xff octets.

    Richard Heylen <richard_in_reading Email address> independently confirmed this partial solution.

  36. Partial solution: What is the shortest set of consecutive 0xff octets for which the 1024-bit FNV-1a hash is 0?
    Peter de Rivaz <peter.derivaz Email address> on 2012-Mar-22 found a 1024-bit solution that may not be the shortest: 
    712131032390661212423469446429778580303529367161714287727915539272088837
    
388997682828851224650621762650604398414532544740385461220466517818153731
    
651665570936392160298954932547331005615954561744064764751259871084045735
    
302812555692177957250787849447135140298017119914349292668850620197682629
    
52245579219890855775 0xff octets.

    Richard Heylen <richard_in_reading Email address> independently confirmed this partial solution.

    NOTE: Russ Cox <rcs Email address> observed that as a consequence of his solution to the consecutive NUL octet challenge, any consecutive stream of 0xff with a zero FNV-1 or FNV-1a hash of any size must be of odd length.

    NOTE: By set of consecutive 0xff octets we mean consecutive octets of 0xff value.

  37. SOLVED! What is the shortest non-NUL ASCII string for which the 32-bit FNV-1 hash is 0?
    32-bit solution by Russ Cox <rcs Email address> on 2011-Mar-02: 
    The solutions of length 5 are:

FNV32_1(07 65 76 4a 3b) = 0    \a e v J ;
FNV32_1(27 0f 56 47 0a) = 0    ' ^O V G \n
FNV32_1(30 17 22 62 62) = 0    0 ^W " b b
FNV32_1(30 33 53 42 5b) = 0    0 3 S B [
FNV32_1(54 20 75 7b 5b) = 0    T space u { [
FNV32_1(62 61 2c 31 71) = 0    b a , 1 q

  38. SOLVED! What is the shortest non-NUL ASCII string for which the 64-bit FNV-1 hash is 0?
    64-bit solution by Peter de Rivaz <peter.derivaz Email address> on 2011-Mar-11: 
    The shortest solution is of length 10:

FNV64_1(10 17 34 7c 28 61 38 72 64 4d) = 0    ^P ^H 4 ! ( a 8 r d M

There are no solutions shorter than length 10.
    Rudi Cilibrasi <cilibrar Email address>, on 2014-Dec-26, verified the above 64-bit solution and found 43 more of the same length: 
    
FNV64_1(0d 20 3f 5c 4f 7e 5e 18 56 64 ) = 0
FNV64_1(11 79 03 18 05 4e 13 3d 6d 74 ) = 0
FNV64_1(12 31 5a 0c 01 04 39 09 30 01 ) = 0
FNV64_1(15 5b 15 18 37 74 55 47 64 6f ) = 0
FNV64_1(21 47 5b 64 66 75 01 59 61 7a ) = 0
FNV64_1(29 28 57 2f 5b 0c 36 70 43 12 ) = 0
FNV64_1(29 78 6c 48 2e 3e 24 7b 10 25 ) = 0
FNV64_1(33 14 71 7d 24 03 6a 67 5c 20 ) = 0
FNV64_1(34 45 09 75 1d 05 6a 78 14 46 ) = 0
FNV64_1(35 46 77 16 38 13 2a 2e 21 4b ) = 0
FNV64_1(36 24 60 55 52 06 7b 60 6a 65 ) = 0
FNV64_1(39 41 05 59 56 32 5c 64 0d 72 ) = 0
FNV64_1(3d 23 1d 04 12 1e 70 38 66 78 ) = 0
FNV64_1(40 61 13 53 2a 14 45 2b 40 68 ) = 0
FNV64_1(44 08 7c 16 2e 1b 65 0d 1e 0a ) = 0
FNV64_1(4c 50 01 3f 50 4f 62 4d 59 5a ) = 0
FNV64_1(61 73 26 4a 71 39 06 47 29 5d ) = 0
FNV64_1(6a 6a 02 16 37 5f 28 53 72 46 ) = 0
FNV64_1(72 31 6f 68 3c 6f 39 0d 66 18 ) = 0
FNV64_1(72 3a 40 76 02 58 35 24 19 29 ) = 0
FNV64_1(01 44 42 05 34 6a 2f 29 31 10 ) = 0
FNV64_1(01 5e 68 02 53 4a 76 3d 1e 78 ) = 0
FNV64_1(04 66 63 3c 0c 4b 70 73 15 09 ) = 0
FNV64_1(0f 45 7c 0b 30 05 18 69 5d 55 ) = 0
FNV64_1(11 15 3d 2e 4c 25 59 30 7f 49 ) = 0
FNV64_1(12 1f 1a 1b 26 02 4a 16 0e 4b ) = 0
FNV64_1(12 2a 1c 09 73 52 7d 08 0c 20 ) = 0
FNV64_1(1c 47 57 23 14 1e 59 74 7a 3f ) = 0
FNV64_1(20 65 5b 68 4a 25 09 34 6c 21 ) = 0
FNV64_1(21 76 29 45 59 77 59 56 6b 26 ) = 0
FNV64_1(25 1d 3f 20 69 20 58 6e 6f 62 ) = 0
FNV64_1(31 30 02 56 05 58 0d 3e 6a 62 ) = 0
FNV64_1(33 69 2a 25 2f 34 06 2f 04 3a ) = 0
FNV64_1(34 1d 36 4e 2f 71 70 50 30 24 ) = 0
FNV64_1(39 04 2d 0f 12 65 01 26 2b 79 ) = 0
FNV64_1(4d 16 6a 48 6c 5e 7e 58 0a 30 ) = 0
FNV64_1(60 09 50 68 4b 21 4f 5b 1f 73 ) = 0
FNV64_1(65 32 24 01 20 44 2a 53 03 7d ) = 0
FNV64_1(65 7e 7c 15 40 13 64 2b 6e 43 ) = 0
FNV64_1(67 51 4f 1d 5c 18 47 03 3f 0a ) = 0
FNV64_1(71 1f 70 0b 78 25 43 0d 08 5b ) = 0
FNV64_1(7a 5f 63 61 14 38 16 10 09 01 ) = 0
FNV64_1(7f 4f 19 62 60 61 6e 16 4b 02 ) = 0

  39. What is the shortest non-NUL ASCII string for which the 128-bit FNV-1 hash is 0?

  40. What is the shortest non-NUL ASCII string for which the 256-bit FNV-1 hash is 0?

  41. What is the shortest non-NUL ASCII string for which the 512-bit FNV-1 hash is 0?

  42. What is the shortest non-NUL ASCII string for which the 1024-bit FNV-1 hash is 0?

  43. SOLVED! What is the shortest non-NUL ASCII string for which the 32-bit FNV-1a hash is 0?
    32-bit solution by Russ Cox <rcs Email address> on 2011-Mar-02: 
    The solutions of length 5 are:

FNV32_1a(12 3b 5b 23 20) = 0    ^R ; [ # space
FNV32_1a(2b 21 3d 79 47) = 0    + ! = y G
FNV32_1a(2f 06 3c 37 71) = 0    / ^F < 7 q
FNV32_1a(36 38 6d 2a 20) = 0    6 8 m * space
FNV32_1a(40 24 1b 38 42) = 0    @ $ Esc 8 B
FNV32_1a(4c 39 59 56 11) = 0    L 9 Y V ^Q
FNV32_1a(59 08 26 60 62) = 0    Y \b & ` b
FNV32_1a(60 4a 63 6f 11) = 0    ` J c o ^Q
FNV32_1a(65 53 4e 2e 31) = 0    e S N . 1

  44. SOLVED? What is the shortest non-NUL ASCII string for which the 64-bit FNV-1a hash is 0?
    64-bit solutions by Rudi Cilibrasi <cilibrar Email address> on 2014-Dec-26 believes there are no other solutions of the same or shorter length: 
    
FNV64_1a(07 1e 62 37 2c 02 40 42 14 69 ) = 0
FNV64_1a(0a 4d 3e 21 16 68 02 0e 0c 6d ) = 0
FNV64_1a(0a 59 59 0e 24 44 2a 7b 60 70 ) = 0
FNV64_1a(0f 73 15 07 1b 6f 38 4b 17 39 ) = 0
FNV64_1a(10 28 59 4f 6d 07 0f 45 3f 2e ) = 0
FNV64_1a(16 43 29 25 71 1b 5c 65 7a 03 ) = 0
FNV64_1a(1c 7f 21 5c 2d 09 1a 03 7f 69 ) = 0
FNV64_1a(21 30 49 43 3d 56 6c 6f 61 59 ) = 0
FNV64_1a(26 04 5d 12 7c 7d 66 61 0c 26 ) = 0
FNV64_1a(3d 2e 20 68 78 22 69 58 3c 3b ) = 0
FNV64_1a(3d 66 7f 2f 6e 36 53 40 30 5d ) = 0
FNV64_1a(42 21 21 7b 16 0e 2f 65 67 25 ) = 0
FNV64_1a(46 2e 24 74 64 6f 3c 01 07 24 ) = 0
FNV64_1a(51 76 58 74 4d 3e 40 46 70 25 ) = 0
FNV64_1a(54 14 18 68 68 4b 14 3c 0a 72 ) = 0
FNV64_1a(58 59 54 4d 5c 4d 45 46 0d 7c ) = 0
FNV64_1a(5f 22 6b 57 6b 3d 2d 76 24 63 ) = 0
FNV64_1a(60 22 10 0e 59 21 65 39 7a 69 ) = 0
FNV64_1a(65 05 78 75 4f 47 3a 15 6a 23 ) = 0
FNV64_1a(65 79 15 0c 1d 73 32 40 5a 26 ) = 0
FNV64_1a(67 2c 21 55 66 46 29 7b 68 04 ) = 0
FNV64_1a(01 1c 4f 49 78 7e 12 6e 6d 61 ) = 0
FNV64_1a(05 46 2b 0d 6f 5f 67 1d 63 49 ) = 0
FNV64_1a(09 1c 11 5b 68 01 09 23 37 48 ) = 0
FNV64_1a(09 5c 02 44 11 06 58 5d 27 3f ) = 0
FNV64_1a(13 67 10 1b 08 30 2a 55 71 2a ) = 0
FNV64_1a(20 0e 75 1d 51 65 72 0a 62 0b ) = 0
FNV64_1a(21 41 46 17 02 63 03 5b 5b 76 ) = 0
FNV64_1a(22 42 59 2e 18 0a 14 6f 57 72 ) = 0
FNV64_1a(2d 64 37 3d 74 48 18 3e 38 4e ) = 0
FNV64_1a(30 5e 64 66 59 24 65 64 5f 06 ) = 0
FNV64_1a(31 51 18 5b 43 5f 3a 6b 60 49 ) = 0
FNV64_1a(36 48 0e 56 31 6f 17 59 38 0d ) = 0
FNV64_1a(3d 03 4f 76 44 69 7b 5b 3d 04 ) = 0
FNV64_1a(4d 1a 06 77 15 33 08 4d 01 21 ) = 0
FNV64_1a(56 1b 0d 31 28 39 04 09 35 63 ) = 0
FNV64_1a(56 35 71 38 31 4a 13 14 74 53 ) = 0
FNV64_1a(5f 01 62 60 20 4f 4a 62 5c 42 ) = 0
FNV64_1a(65 68 4f 66 68 21 3b 07 06 02 ) = 0
FNV64_1a(69 59 67 0c 2a 65 07 0d 46 0d ) = 0
FNV64_1a(69 5c 69 45 1a 78 3f 7b 49 21 ) = 0
FNV64_1a(6c 03 4c 6c 0f 05 4a 4e 7c 1c ) = 0
FNV64_1a(6c 38 33 4a 46 30 40 15 60 63 ) = 0
FNV64_1a(6c 55 0c 32 30 01 28 2f 2d 25 ) = 0
FNV64_1a(6e 09 5a 3a 1d 2b 63 77 16 44 ) = 0
FNV64_1a(6e 70 20 3e 33 19 4a 0f 07 77 ) = 0
FNV64_1a(7a 47 54 16 6e 75 42 78 2f 48 ) = 0
FNV64_1a(7b 3e 68 34 5f 71 43 2a 13 12 ) = 0

  45. What is the shortest non-NUL ASCII string for which the 128-bit FNV-1a hash is 0?

  46. What is the shortest non-NUL ASCII string for which the 256-bit FNV-1a hash is 0?

  47. What is the shortest non-NUL ASCII string for which the 512-bit FNV-1a hash is 0?

  48. What is the shortest non-NUL ASCII string for which the 1024-bit FNV-1a hash is 0?

    NOTE: By non-NUL ASCII string we mean any arbitrary collection of non-NUL ASCII 8-bit characters in the range: [0x01 - 0x7f]. Obviously the C-style terminating NUL octet is not included.

  49. SOLVED! What is the shortest printable ASCII string for which the 32-bit FNV-1 hash is 0?
    32-bit hash solution by Russ Cox <rcs Email address> on 2011-Mar-02: 
    The solutions of length 5 are:

FNV32_1(30 33 53 42 5b) = 0    0 3 S B [
FNV32_1(54 20 75 7b 5b) = 0    T Space u { [
FNV32_1(62 61 2c 31 71) = 0    b a , 1 q

  50. SOLVED? What is the shortest printable ASCII string for which the 64-bit FNV-1 hash is 0?
    64-bit solution by Rudi Cilibrasi <cilibrar Email address> on 2014-Dec-26 believes there are no other solutions of the same or shorter length: 
    
FNV64_1(21 76 29 45 59 77 59 56 6b 26) = 0    !v)EYwYVk&

  51. What is the shortest printable ASCII string for which the 128-bit FNV-1 hash is 0?

  52. What is the shortest printable ASCII string for which the 256-bit FNV-1 hash is 0?

  53. What is the shortest printable ASCII string for which the 512-bit FNV-1 hash is 0?

  54. What is the shortest printable ASCII string for which the 1024-bit FNV-1 hash is 0?

  55. SOLVED! What is the shortest printable ASCII string for which the 32-bit FNV-1a hash is 0?
    32-bit hash solution by Russ Cox <rcs Email address> on 2011-Mar-02: 
    The solutions of length 5 are:

FNV32_1a(2b 21 3d 79 47) = 0    + ! = y G
FNV32_1a(36 38 6d 2a 20) = 0    6 8 m * Space
FNV32_1a(65 53 4e 2e 31) = 0    e S N . 1

  56. SOLVED? What is the shortest printable ASCII string for which the 64-bit FNV-1a hash is 0?
    64-bit solutions by Rudi Cilibrasi <cilibrar Email address> on 2014-Dec-26 believes there are no other solutions of the same or shorter length: 
    
FNV64_1a(21 30 49 43 3d 56 6c 6f 61 59) = 0    !0IC=VloaY
FNV64_1a(3d 2e 20 68 78 22 69 58 3c 3b) = 0    =. hx"iX<;
FNV64_1a(51 76 58 74 4d 3e 40 46 70 25) = 0    QvXtM%gt;@Fp%
FNV64_1a(5f 22 6b 57 6b 3d 2d 76 24 63) = 0    _"kWk=-v$c

  57. What is the shortest printable ASCII string for which the 128-bit FNV-1a hash is 0?

  58. What is the shortest printable ASCII string for which the 256-bit FNV-1a hash is 0?

  59. What is the shortest printable ASCII string for which the 512-bit FNV-1a hash is 0?

  60. What is the shortest printable ASCII string for which the 1024-bit FNV-1a hash is 0?

    NOTE: By printable ASCII string we mean any arbitrary collection of printable ASCII 8-bit characters in the range: [0x20 - 0x7e]. Obviously the C-style terminating NUL octet is not included.

  61. SOLVED! What is the shortest alphanumeric ASCII string for which the 32-bit FNV-1 hash is 0?
    32-bit hash solution by Russ Cox <rcs Email address> on 2011-Mar-02: 
    The solutions of length 6 are:


FNV32_1(33 64 37 41 35 4b) = 0    3 d 7 A 5 K
FNV32_1(39 71 36 4d 71 33) = 0    9 q 6 M q 3
FNV32_1(48 48 59 53 4c 45) = 0    H H Y S L E
FNV32_1(54 72 4c 64 5a 31) = 0    T r L d Z 1
FNV32_1(56 4c 33 42 71 43) = 0    V L 3 B q C
FNV32_1(57 41 64 32 60 57) = 0    W A d 2 ` W
FNV32_1(59 55 6f 31 39 6c) = 0    Y U o 1 9 l
FNV32_1(59 66 36 68 50 36) = 0    Y f 6 h P 6
FNV32_1(68 49 72 6a 46 6a) = 0    h I r j F j
FNV32_1(6e 60 62 76 33 52) = 0    n ` b v 3 R
FNV32_1(70 6c 49 7a 6c 60) = 0    p l I z l `
FNV32_1(75 4d 6b 60 39 51) = 0    u M k ` 9 Q
FNV32_1(79 73 6f 70 48 6c) = 0    y s o p H l
FNV32_1(7a 63 49 6b 43 65) = 0    z c I k C e

  62. SOLVED? What is the shortest alphanumeric ASCII string for which the 64-bit FNV-1 hash is 0?
    64-bit solutions by Rudi Cilibrasi <cilibrar Email address> on 2014-Dec-26 believes there are no other solutions of the same or shorter length: 
    
FNV64_1(4d 74 35 4b 65 78 6e 79 33 31 6e) = 0    Mt5Kexny31n
FNV64_1(4f 6a 53 48 6a 69 6b 50 4e 59 56) = 0    OjSHjikPNYV
FNV64_1(59 49 41 39 59 57 4d 4f 41 52 58) = 0    YIA9YWMOARX

  63. What is the shortest alphanumeric ASCII string for which the 128-bit FNV-1 hash is 0?

  64. What is the shortest alphanumeric ASCII string for which the 256-bit FNV-1 hash is 0?

  65. What is the shortest alphanumeric ASCII string for which the 512-bit FNV-1 hash is 0?

  66. What is the shortest alphanumeric ASCII string for which the 1024-bit FNV-1 hash is 0?

  67. SOLVED! What is the shortest alphanumeric ASCII string for which the 32-bit FNV-1a hash is 0?
    32-bit hash solution by Russ Cox <rcs Email address> on 2011-Mar-02: 
    The solutions of length 6 are:

FNV32_1a(33 70 6a 4e 71 4d) = 0    3 p j N q M
FNV32_1a(35 52 30 4c 67 37) = 0    5 R 0 L g 7
FNV32_1a(37 6f 45 34 38 36) = 0    7 o E 4 8 6
FNV32_1a(42 52 34 32 71 66) = 0    B R 4 2 q f
FNV32_1a(46 6f 75 42 53 72) = 0    F o u B S r
FNV32_1a(47 6b 6b 7a 46 44) = 0    G k k z F D
FNV32_1a(48 56 47 5a 71 39) = 0    H V G Z q 9
FNV32_1a(49 77 50 53 64 54) = 0    I w P S d T
FNV32_1a(60 6e 72 59 33 47) = 0    ` n r Y 3 G
FNV32_1a(71 7a 73 30 55 44) = 0    q z s 0 U D
FNV32_1a(73 58 62 73 73 72) = 0    s X b s s r
FNV32_1a(75 68 34 74 53 49) = 0    u h 4 t S I

  68. SOLVED? What is the shortest alphanumeric ASCII string for which the 64-bit FNV-1a hash is 0?
    64-bit solution by Rudi Cilibrasi <cilibrar Email address> on 2014-Dec-26 believes there are no other solutions of the same or shorter length: 
    
FNV64_1a(37 37 6b 65 70 51 46 51 38 4b 6c) = 0    77kepQFQ8Kl

  69. What is the shortest alphanumeric ASCII string for which the 128-bit FNV-1a hash is 0?

  70. What is the shortest alphanumeric ASCII string for which the 256-bit FNV-1a hash is 0?

  71. What is the shortest alphanumeric ASCII string for which the 512-bit FNV-1a hash is 0?

  72. What is the shortest alphanumeric ASCII string for which the 1024-bit FNV-1a hash is 0?

    NOTE: By alphanumeric ASCII string we mean any arbitrary collection of alphanumeric ASCII 8-bit characters in the range: [0x30 - 0x39, 0x41 - 0x5a, 0x60 - 0x7a] Obviously the C-style terminating NUL octet is not included.





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