Advances in Number Theory

Charles Pooh
Algorithms R&D, Wolfram Research

Advances in Number Theory

Usability

Scope

Performance

PrimePi: Usability

Learnability: Documentation

[PrimePi] [Prime] [NextPrime] [RandomPrime] [PrimeQ]

Ease of Use: Progress Reporting & User Control

PrimePi: Scope

Limits

PrimePi[2.5*10^14]

State of the Art Algorithms

PrimePi[10^15]

PrimePi: Performance

PrimePi[(10^n)] : Version 12 vs 12.1

Known Algorithms

Prime

Scope

Prime[10^13]

Performance

RandomPrime

Uniform Sampling up to (10^10)

randomprime[min_,max_,n_]:=Prime[RandomInteger[{PrimePi[min]+1,PrimePi[max]},n]]

PrimeQ

What’s next?

Usability

Scope

Performance