A Java implementation of the MT19937 (Mersenne Twister) pseudo random number generator algorithm based upon the original C code by Makoto Matsumoto and Takuji Nishimura (see http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html for more information). Read the API documentation.
This class should provide a dependency free drop-in replacement for java.util.Random with the additional
advantage of having a far longer period, and the ability to use a far larger seed value.
This is not a cryptographically strong source of randomness and should not be used for cryptographic systems or in any other situation where true randomness is required.
Version 1.1 is an update to the original code from 2005 and changes a few small things:
- Default seed initialization is no longer based solely on the system clock.
- Unnecessary calls to "setSeed()" during parent class initialization are now ignored.
- Improved JavaDoc documentation.
- Minor code tidying.
Additionally, this version comes with unit tests and a "golden data" test to ensure stability!
The class has also been tested with the random number test suite described at http://csrc.nist.gov/groups/ST/toolkit/random_number.html and http://csrc.nist.gov/groups/ST/toolkit/rng/documents/SP800-22rev1a.pdf.
The test suite used is https://github.com/stamfest/randomtests, written by Peter Stamfest (but this cannot be shipped as a dependenchy of this project for technical and licensing reasons).
The NIST test suite was run for 10 sequences of length 1,000,000 digits, and the results are:
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RESULTS FOR THE UNIFORMITY OF P-VALUES AND THE PROPORTION OF PASSING SEQUENCES
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C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 P-VALUE PROPORTION STATISTICAL TEST
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1 1 0 1 1 2 1 1 1 1 0.991468 10/10 Frequency
0 1 2 2 1 0 0 2 1 1 0.739918 10/10 BlockFrequency(128)
0 2 1 0 1 1 0 1 1 3 0.534146 10/10 CumulativeSums[forward]
0 2 0 2 0 1 0 2 1 2 0.534146 10/10 CumulativeSums[backward]
1 0 1 1 1 3 2 0 1 0 0.534146 10/10 Runs
2 2 1 2 0 1 0 0 1 1 0.739918 10/10 LongestRunOfOnes
2 1 1 1 0 1 1 1 2 0 0.911413 10/10 Rank
1 1 1 2 1 2 0 1 0 1 0.911413 10/10 DiscreteFourierTransform
0 1 0 2 1 1 0 1 2 2 0.739918 10/10 NonOverlappingTemplateMatchings(9)[000000001]
1 0 1 1 0 1 1 1 1 3 0.739918 10/10 NonOverlappingTemplateMatchings(9)[000000011]
0 2 1 4 0 0 0 1 1 1 0.122325 10/10 NonOverlappingTemplateMatchings(9)[000000101]
0 0 4 1 1 0 3 0 0 1 0.035174 10/10 NonOverlappingTemplateMatchings(9)[000000111]
0 3 1 0 2 0 1 2 1 0 0.350485 10/10 NonOverlappingTemplateMatchings(9)[000001001]
3 0 1 1 0 0 1 0 4 0 0.035174 9/10 NonOverlappingTemplateMatchings(9)[000001011]
0 2 1 0 0 2 1 2 0 2 0.534146 10/10 NonOverlappingTemplateMatchings(9)[000001101]
1 0 0 1 1 3 0 0 2 2 0.350485 10/10 NonOverlappingTemplateMatchings(9)[000001111]
0 0 2 5 0 0 1 1 1 0 0.008879 10/10 NonOverlappingTemplateMatchings(9)[000010001]
0 1 0 0 1 4 2 0 1 1 0.122325 10/10 NonOverlappingTemplateMatchings(9)[000010011]
0 1 1 0 1 1 0 2 0 4 0.122325 10/10 NonOverlappingTemplateMatchings(9)[000010101]
0 2 1 1 0 0 2 2 1 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[000010111]
2 0 1 1 1 1 2 1 1 0 0.911413 10/10 NonOverlappingTemplateMatchings(9)[000011001]
0 2 1 0 1 0 1 1 1 3 0.534146 10/10 NonOverlappingTemplateMatchings(9)[000011011]
2 0 0 0 1 1 3 0 1 2 0.350485 10/10 NonOverlappingTemplateMatchings(9)[000011101]
2 1 3 0 0 2 1 0 0 1 0.350485 10/10 NonOverlappingTemplateMatchings(9)[000011111]
1 0 1 1 0 2 1 2 1 1 0.911413 10/10 NonOverlappingTemplateMatchings(9)[000100011]
0 2 1 1 2 2 0 0 1 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[000100101]
1 2 1 1 0 1 2 0 1 1 0.911413 10/10 NonOverlappingTemplateMatchings(9)[000100111]
1 1 1 1 1 2 0 1 0 2 0.911413 10/10 NonOverlappingTemplateMatchings(9)[000101001]
0 1 0 1 1 2 2 1 1 1 0.911413 10/10 NonOverlappingTemplateMatchings(9)[000101011]
0 2 0 0 1 2 1 3 1 0 0.350485 10/10 NonOverlappingTemplateMatchings(9)[000101101]
2 0 2 1 0 1 2 0 0 2 0.534146 10/10 NonOverlappingTemplateMatchings(9)[000101111]
1 2 1 0 2 0 0 0 1 3 0.350485 10/10 NonOverlappingTemplateMatchings(9)[000110011]
1 3 2 0 1 1 0 0 1 1 0.534146 10/10 NonOverlappingTemplateMatchings(9)[000110101]
0 0 2 3 0 0 0 2 2 1 0.213309 10/10 NonOverlappingTemplateMatchings(9)[000110111]
1 0 1 2 2 2 1 1 0 0 0.739918 10/10 NonOverlappingTemplateMatchings(9)[000111001]
0 0 1 0 4 2 1 0 1 1 0.122325 10/10 NonOverlappingTemplateMatchings(9)[000111011]
2 1 0 0 1 3 0 0 2 1 0.350485 10/10 NonOverlappingTemplateMatchings(9)[000111101]
1 4 0 1 3 0 0 1 0 0 0.035174 10/10 NonOverlappingTemplateMatchings(9)[000111111]
2 1 0 0 1 1 1 1 2 1 0.911413 10/10 NonOverlappingTemplateMatchings(9)[001000011]
1 1 1 0 2 2 1 1 1 0 0.911413 10/10 NonOverlappingTemplateMatchings(9)[001000101]
2 2 1 0 1 0 0 2 1 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[001000111]
3 0 1 2 2 0 0 0 0 2 0.213309 10/10 NonOverlappingTemplateMatchings(9)[001001011]
1 1 2 0 2 1 1 1 1 0 0.911413 10/10 NonOverlappingTemplateMatchings(9)[001001101]
3 1 0 1 2 1 0 1 0 1 0.534146 9/10 NonOverlappingTemplateMatchings(9)[001001111]
1 3 1 1 1 1 0 0 1 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[001010011]
3 0 2 0 0 0 0 0 3 2 0.066882 10/10 NonOverlappingTemplateMatchings(9)[001010101]
1 3 0 1 0 1 1 1 1 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[001010111]
2 0 2 0 0 1 1 1 1 2 0.739918 10/10 NonOverlappingTemplateMatchings(9)[001011011]
1 0 0 1 2 0 0 5 1 0 0.008879 10/10 NonOverlappingTemplateMatchings(9)[001011101]
3 2 1 0 1 1 0 0 1 1 0.534146 10/10 NonOverlappingTemplateMatchings(9)[001011111]
1 0 2 2 2 0 1 2 0 0 0.534146 10/10 NonOverlappingTemplateMatchings(9)[001100101]
1 2 2 2 1 0 0 1 0 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[001100111]
1 0 0 1 3 3 0 0 2 0 0.122325 10/10 NonOverlappingTemplateMatchings(9)[001101011]
0 2 3 0 1 0 0 1 1 2 0.350485 10/10 NonOverlappingTemplateMatchings(9)[001101101]
1 0 2 1 0 2 0 1 1 2 0.739918 10/10 NonOverlappingTemplateMatchings(9)[001101111]
1 3 2 0 0 1 0 2 1 0 0.350485 10/10 NonOverlappingTemplateMatchings(9)[001110101]
1 1 0 1 0 2 2 2 0 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[001110111]
0 1 1 2 1 1 2 0 1 1 0.911413 10/10 NonOverlappingTemplateMatchings(9)[001111011]
0 4 0 2 1 1 0 1 0 1 0.122325 10/10 NonOverlappingTemplateMatchings(9)[001111101]
2 0 0 1 2 2 0 1 1 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[001111111]
1 2 0 1 2 1 1 0 2 0 0.739918 10/10 NonOverlappingTemplateMatchings(9)[010000011]
1 0 0 2 3 1 3 0 0 0 0.122325 10/10 NonOverlappingTemplateMatchings(9)[010000111]
1 1 0 0 2 3 0 0 2 1 0.350485 9/10 NonOverlappingTemplateMatchings(9)[010001011]
0 1 0 1 1 2 3 1 0 1 0.534146 10/10 NonOverlappingTemplateMatchings(9)[010001111]
1 2 1 1 0 1 1 0 2 1 0.911413 10/10 NonOverlappingTemplateMatchings(9)[010010011]
1 1 0 3 1 1 0 0 1 2 0.534146 9/10 NonOverlappingTemplateMatchings(9)[010010111]
2 0 1 0 0 1 1 4 0 1 0.122325 8/10 NonOverlappingTemplateMatchings(9)[010011011]
1 0 0 1 0 2 2 2 1 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[010011111]
1 1 1 0 0 2 2 1 2 0 0.739918 10/10 NonOverlappingTemplateMatchings(9)[010100011]
1 3 0 1 0 0 2 0 1 2 0.350485 10/10 NonOverlappingTemplateMatchings(9)[010100111]
1 4 1 1 2 0 0 1 0 0 0.122325 10/10 NonOverlappingTemplateMatchings(9)[010101011]
2 1 1 2 1 1 1 0 1 0 0.911413 10/10 NonOverlappingTemplateMatchings(9)[010101111]
0 1 3 2 0 2 1 0 0 1 0.350485 10/10 NonOverlappingTemplateMatchings(9)[010110011]
0 1 0 2 3 0 0 1 3 0 0.122325 10/10 NonOverlappingTemplateMatchings(9)[010110111]
2 1 0 1 0 1 0 0 4 1 0.122325 9/10 NonOverlappingTemplateMatchings(9)[010111011]
1 4 1 1 0 0 1 1 0 1 0.213309 10/10 NonOverlappingTemplateMatchings(9)[010111111]
3 1 0 0 0 1 2 0 3 0 0.122325 10/10 NonOverlappingTemplateMatchings(9)[011000111]
1 1 1 2 1 2 1 1 0 0 0.911413 9/10 NonOverlappingTemplateMatchings(9)[011001111]
1 1 1 0 2 2 2 0 0 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[011010111]
1 1 1 0 0 1 1 3 0 2 0.534146 10/10 NonOverlappingTemplateMatchings(9)[011011111]
0 0 2 2 1 2 2 0 1 0 0.534146 10/10 NonOverlappingTemplateMatchings(9)[011101111]
1 1 0 2 1 0 0 1 0 4 0.122325 10/10 NonOverlappingTemplateMatchings(9)[011111111]
0 1 0 2 1 1 0 1 2 2 0.739918 10/10 NonOverlappingTemplateMatchings(9)[100000000]
2 2 0 0 0 1 3 1 0 1 0.350485 10/10 NonOverlappingTemplateMatchings(9)[100010000]
1 0 3 0 0 4 0 1 0 1 0.035174 9/10 NonOverlappingTemplateMatchings(9)[100100000]
2 0 0 0 1 3 1 1 1 1 0.534146 10/10 NonOverlappingTemplateMatchings(9)[100101000]
1 1 1 0 0 3 0 1 1 2 0.534146 10/10 NonOverlappingTemplateMatchings(9)[100110000]
3 0 0 1 1 2 2 0 1 0 0.350485 10/10 NonOverlappingTemplateMatchings(9)[100111000]
3 0 0 2 0 1 0 2 0 2 0.213309 10/10 NonOverlappingTemplateMatchings(9)[101000000]
2 0 2 1 1 0 1 1 1 1 0.911413 10/10 NonOverlappingTemplateMatchings(9)[101000100]
0 0 3 3 1 0 0 2 0 1 0.122325 10/10 NonOverlappingTemplateMatchings(9)[101001000]
0 2 1 0 0 2 1 1 2 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[101001100]
2 0 2 0 2 2 1 1 0 0 0.534146 10/10 NonOverlappingTemplateMatchings(9)[101010000]
0 1 1 1 0 0 0 4 1 2 0.122325 10/10 NonOverlappingTemplateMatchings(9)[101010100]
0 2 1 0 2 0 2 0 3 0 0.213309 10/10 NonOverlappingTemplateMatchings(9)[101011000]
1 1 1 2 0 0 1 0 1 3 0.534146 10/10 NonOverlappingTemplateMatchings(9)[101011100]
2 1 1 2 0 2 0 0 1 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[101100000]
1 0 1 3 1 0 1 1 0 2 0.534146 10/10 NonOverlappingTemplateMatchings(9)[101100100]
1 4 1 0 1 1 1 0 1 0 0.213309 10/10 NonOverlappingTemplateMatchings(9)[101101000]
2 0 0 0 1 2 2 2 0 1 0.534146 10/10 NonOverlappingTemplateMatchings(9)[101101100]
1 0 1 0 0 1 1 3 3 0 0.213309 10/10 NonOverlappingTemplateMatchings(9)[101110000]
3 1 0 1 0 0 1 2 1 1 0.534146 10/10 NonOverlappingTemplateMatchings(9)[101110100]
1 1 0 1 0 0 2 2 1 2 0.739918 10/10 NonOverlappingTemplateMatchings(9)[101111000]
1 1 1 1 1 3 0 0 0 2 0.534146 10/10 NonOverlappingTemplateMatchings(9)[101111100]
0 0 1 0 2 0 1 2 1 3 0.350485 10/10 NonOverlappingTemplateMatchings(9)[110000000]
1 0 0 0 1 1 1 1 4 1 0.213309 10/10 NonOverlappingTemplateMatchings(9)[110000010]
0 0 1 1 0 5 0 2 0 1 0.008879 10/10 NonOverlappingTemplateMatchings(9)[110000100]
1 0 1 0 3 0 2 3 0 0 0.122325 10/10 NonOverlappingTemplateMatchings(9)[110001000]
0 2 2 1 0 2 0 2 1 0 0.534146 10/10 NonOverlappingTemplateMatchings(9)[110001010]
1 1 1 0 1 3 0 1 1 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[110010000]
1 1 0 1 1 1 0 1 1 3 0.739918 10/10 NonOverlappingTemplateMatchings(9)[110010010]
1 3 1 0 0 1 1 2 1 0 0.534146 10/10 NonOverlappingTemplateMatchings(9)[110010100]
0 1 1 1 2 4 0 0 1 0 0.122325 10/10 NonOverlappingTemplateMatchings(9)[110011000]
3 0 0 0 1 2 2 1 0 1 0.350485 9/10 NonOverlappingTemplateMatchings(9)[110011010]
0 2 1 0 1 2 1 1 1 1 0.911413 10/10 NonOverlappingTemplateMatchings(9)[110100000]
4 0 1 2 0 1 2 0 0 0 0.066882 8/10 NonOverlappingTemplateMatchings(9)[110100010]
0 1 1 2 1 1 1 2 0 1 0.911413 10/10 NonOverlappingTemplateMatchings(9)[110100100]
2 1 0 0 1 0 3 0 2 1 0.350485 9/10 NonOverlappingTemplateMatchings(9)[110101000]
0 0 1 1 3 2 0 1 1 1 0.534146 10/10 NonOverlappingTemplateMatchings(9)[110101010]
0 1 0 1 4 2 1 0 1 0 0.122325 10/10 NonOverlappingTemplateMatchings(9)[110101100]
2 0 1 2 0 1 1 1 1 1 0.911413 10/10 NonOverlappingTemplateMatchings(9)[110110000]
2 2 1 0 0 1 0 1 1 2 0.739918 9/10 NonOverlappingTemplateMatchings(9)[110110010]
1 0 2 0 3 1 2 0 1 0 0.350485 10/10 NonOverlappingTemplateMatchings(9)[110110100]
1 1 1 1 0 4 0 0 0 2 0.122325 10/10 NonOverlappingTemplateMatchings(9)[110111000]
2 0 1 0 0 2 1 1 2 1 0.739918 9/10 NonOverlappingTemplateMatchings(9)[110111010]
0 0 2 0 1 2 0 0 1 4 0.066882 10/10 NonOverlappingTemplateMatchings(9)[110111100]
0 3 0 2 1 0 2 0 1 1 0.350485 10/10 NonOverlappingTemplateMatchings(9)[111000000]
0 0 2 4 0 0 1 0 2 1 0.066882 10/10 NonOverlappingTemplateMatchings(9)[111000010]
1 1 0 0 0 2 3 1 1 1 0.534146 10/10 NonOverlappingTemplateMatchings(9)[111000100]
1 2 0 0 1 1 0 1 2 2 0.739918 10/10 NonOverlappingTemplateMatchings(9)[111000110]
0 0 2 2 0 3 1 1 1 0 0.350485 10/10 NonOverlappingTemplateMatchings(9)[111001000]
2 1 2 0 1 0 1 2 1 0 0.739918 10/10 NonOverlappingTemplateMatchings(9)[111001010]
0 2 0 2 0 0 2 1 2 1 0.534146 10/10 NonOverlappingTemplateMatchings(9)[111001100]
3 2 1 1 1 1 0 0 1 0 0.534146 10/10 NonOverlappingTemplateMatchings(9)[111010000]
1 1 2 1 1 0 3 0 1 0 0.534146 10/10 NonOverlappingTemplateMatchings(9)[111010010]
1 1 1 2 0 0 2 3 0 0 0.350485 10/10 NonOverlappingTemplateMatchings(9)[111010100]
1 2 0 1 0 2 1 0 2 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[111010110]
2 1 1 1 2 1 0 0 0 2 0.739918 10/10 NonOverlappingTemplateMatchings(9)[111011000]
0 1 2 0 0 2 1 2 1 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[111011010]
3 0 2 2 1 2 0 0 0 0 0.213309 9/10 NonOverlappingTemplateMatchings(9)[111011100]
0 1 0 3 0 3 0 1 2 0 0.122325 10/10 NonOverlappingTemplateMatchings(9)[111100000]
0 2 0 1 0 1 0 2 0 4 0.066882 10/10 NonOverlappingTemplateMatchings(9)[111100010]
2 1 2 1 1 0 0 1 2 0 0.739918 10/10 NonOverlappingTemplateMatchings(9)[111100100]
1 0 3 1 1 2 1 1 0 0 0.534146 10/10 NonOverlappingTemplateMatchings(9)[111100110]
2 0 0 2 0 1 0 1 4 0 0.066882 10/10 NonOverlappingTemplateMatchings(9)[111101000]
1 1 0 0 1 4 0 2 0 1 0.122325 10/10 NonOverlappingTemplateMatchings(9)[111101010]
1 1 0 2 0 1 1 2 1 1 0.911413 10/10 NonOverlappingTemplateMatchings(9)[111101100]
0 0 3 2 0 0 2 0 2 1 0.213309 10/10 NonOverlappingTemplateMatchings(9)[111101110]
1 1 1 1 0 3 0 1 2 0 0.534146 9/10 NonOverlappingTemplateMatchings(9)[111110000]
4 0 1 1 1 3 0 0 0 0 0.035174 10/10 NonOverlappingTemplateMatchings(9)[111110010]
3 0 2 1 0 0 1 2 1 0 0.350485 10/10 NonOverlappingTemplateMatchings(9)[111110100]
0 1 0 1 1 0 1 0 3 3 0.213309 10/10 NonOverlappingTemplateMatchings(9)[111110110]
2 2 1 1 0 2 0 0 1 1 0.739918 10/10 NonOverlappingTemplateMatchings(9)[111111000]
3 1 3 1 1 0 0 0 0 1 0.213309 10/10 NonOverlappingTemplateMatchings(9)[111111010]
0 2 0 0 1 1 2 1 1 2 0.739918 10/10 NonOverlappingTemplateMatchings(9)[111111100]
1 1 0 2 1 0 0 1 0 4 0.122325 10/10 NonOverlappingTemplateMatchings(9)[111111110]
0 5 0 0 2 1 1 0 0 1 0.008879 10/10 OverlappingTemplateMatching(9)
0 1 0 2 1 3 1 0 1 1 0.534146 10/10 Universal
2 0 1 0 1 1 2 0 2 1 0.739918 10/10 ApproximateEntropy(10)
1 0 0 2 0 0 4 0 0 1 ---- 8/8 RandomExcursions[-4]
1 0 1 1 0 2 1 0 0 2 ---- 8/8 RandomExcursions[-3]
0 2 2 1 0 2 0 0 0 1 ---- 8/8 RandomExcursions[-2]
1 0 0 0 1 0 2 1 1 2 ---- 8/8 RandomExcursions[-1]
2 0 0 0 0 1 2 2 0 1 ---- 8/8 RandomExcursions[1]
3 1 0 0 0 1 2 0 1 0 ---- 8/8 RandomExcursions[2]
1 2 3 1 0 0 0 1 0 0 ---- 8/8 RandomExcursions[3]
1 2 1 0 0 0 3 0 1 0 ---- 8/8 RandomExcursions[4]
1 0 0 1 1 2 0 2 0 1 ---- 8/8 RandomExcursionsVariant[-9]
0 1 0 1 0 3 1 0 1 1 ---- 8/8 RandomExcursionsVariant[-8]
0 1 0 1 1 2 1 1 1 0 ---- 8/8 RandomExcursionsVariant[-7]
0 1 0 2 3 2 0 0 0 0 ---- 8/8 RandomExcursionsVariant[-6]
1 1 1 2 0 2 0 0 1 0 ---- 8/8 RandomExcursionsVariant[-5]
2 0 1 2 1 0 0 0 0 2 ---- 8/8 RandomExcursionsVariant[-4]
1 2 1 0 1 0 2 0 0 1 ---- 8/8 RandomExcursionsVariant[-3]
1 0 3 1 0 0 2 1 0 0 ---- 8/8 RandomExcursionsVariant[-2]
0 2 1 0 1 1 1 1 0 1 ---- 8/8 RandomExcursionsVariant[-1]
0 0 2 2 2 0 0 1 1 0 ---- 8/8 RandomExcursionsVariant[1]
0 3 1 1 1 0 0 1 1 0 ---- 8/8 RandomExcursionsVariant[2]
1 3 0 1 0 0 1 0 0 2 ---- 8/8 RandomExcursionsVariant[3]
1 1 1 1 1 0 1 1 0 1 ---- 8/8 RandomExcursionsVariant[4]
0 2 2 0 0 2 1 0 0 1 ---- 8/8 RandomExcursionsVariant[5]
1 1 0 0 0 2 3 0 0 1 ---- 8/8 RandomExcursionsVariant[6]
1 1 0 0 0 1 0 2 1 2 ---- 8/8 RandomExcursionsVariant[7]
1 1 0 0 1 0 2 2 0 1 ---- 8/8 RandomExcursionsVariant[8]
1 1 0 0 1 1 2 0 0 2 ---- 8/8 RandomExcursionsVariant[9]
0 0 2 2 3 1 2 0 0 0 0.213309 10/10 Serial(16)[1]
1 0 3 3 0 1 1 1 0 0 0.213309 10/10 Serial(16)[2]
0 1 1 1 1 3 0 1 0 2 0.534146 10/10 LinearComplexity(500)
Interpreting the results is not trivial, and the tests are (by their nature) non-repeatable, but the summary shows
that for each test all, or almost all, of the sequences tested satisfy the test criteria (e.g. 9/10 or 10/10).
A random sequence can always exhibit apparent "structure" purely by chance, so having a small number of sequences "fail" is not unexpected. What's important is that for all tests, over multiple runs, most sequences pass.