Math-Prime-Util

Changes for version 0.61 - 2017-03-12

ADDED
- is_semiprime(n) Returns 1 if n has exactly 2 prime factors
- is_pillai(p) Returns 0 or v wherev v! % n == n-1 and n % v != 1
- inverse_li(n) Integer inverse of Logarithmic Integral
FUNCTIONALITY AND PERFORMANCE
- is_power(-1,k) now returns true for odd k.
- RiemannZeta with GMP was not subtracting 1 from results > 9.
- PP Bernoulli algorithm changed to Seidel from Brent-Harvey. 2x speedup. Math::BigNum is 10x faster, and our GMP code is 2000x faster.
- LambertW changes in C and PP. Much better initial approximation, and switch iteration from Halley to Fritsch. 2 to 10x faster.
- Try to use GMP LambertW for bignums if it is available.
- Use Montgomery math in more places:
  - sqrtmod. 1.2-1.7x faster.
  - is_primitive_root. Up to 2x faster for some inputs.
  - p-1 factoring stage 1.
- Tune AKS r/s selection above 32-bit.
- primes.pl uses twin_primes function for ~3x speedup.
- native chinese can handle some cases that used to overflow. Use Shell sort on moduli to prevent pathological-but-reasonable test case.
- chinese directly to GMP
- Switch to Bytes::Random::Secure::Tiny -- fewer dependencies.
- PP nth_prime_approx has better MSE and uses inverse_li above 10^12.
- All random prime functions will use GMP versions if possible and if a custom irand has not been configured. They are much faster than the PP versions at smaller bit sizes.
- is_carmichael and is_pillai small speedups.

Utilities related to prime numbers, including fast sieves and factoring

Elliptic curve operations for affine points

Elliptic curve operations for projective points

An auto-free object for Math::Prime::Util

Pure Perl version of Math::Prime::Util

PP front end for Math::Prime::Util

Primality proofs and certificates

A tied array for primes

An object iterator for primes

Generate random primes

Generate random primes using MPU::GMP

Perl Big Float versions of Riemann Zeta and R functions

Number theory utilities

To install Math::Prime::Util, copy and paste the appropriate command in to your terminal.

cpanm Math::Prime::Util

perl -MCPAN -e shell
install Math::Prime::Util

For more information on module installation, please visit the detailed CPAN module installation guide.

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