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Mark Rodenkirch's MultiSieve.exe


A titan, as defined by Samuel Yates, is anyone who has found a titanic prime. This page provides data on those that have found these primes. The data below only reflect on the primes currently on the list. (Many of the terms that are used here are explained on another page.)

p75, p77, p93, p95, p99 ... ... L4780, L4784, p402, L4972, L5116
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Username: MultiSieve (entry created on 01/22/2003)
Database id:449 (entry last modified on 07/07/2020)
Program Does *: sieve
Active primes:on current list: 34, rank by number 17
Total primes: number ever on any list: 284
Production score: for current list 52 (normalized: 3188), total 52.3460, rank by score 15
Largest prime: 8508301 · 217016603 - 1 ‏(‎5122515 digits) via code L4784 on 03/22/2018
Most recent: 191547657 · 2173372 + 1 ‏(‎52199 digits) via code L5116 on 07/07/2020
Entrance Rank: mean 3676.91 (minimum 13, maximum 53674)

Descriptive Data: (report abuse)

This program is used for sieving numbers of some popular forms that are not supported in NewPGen or any of the other popular sieves. This includes:

  • factorials (n!+/-1)
  • multi-factorials (n!x+/-1 for x > 1, e.g. n!5+1 = n!!!!!+1)
  • primorial (p# +/- 1)
  • Cullens/Woodalls (n*2^n+/-1)
  • Generalized Cullens/Woodalls (n*b^n+/-1 for b > 2), x^y+y^x
  • Cylotomics of factorial/multifactorial form (Phi(a, n!) and Phi(a, n!x) for a <= 24)
  • Carol/Kynea (2^n +/- 1)^2 - 2
  • x^y + y^x
  • k*b^b +/- 1
  • Hyper Cullen/Woodall k^b*b^k +/- 1
  • Near Cullent/Woodall (k +/- 1)*b^k +/- 1

MultiSieve is no longer supported. It has been replaced by the mtsieve framework

Surname: MultiSieve (used for alphabetizing and in codes)
Unverified primes are omitted from counts and lists until verification completed.
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