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Re: [PrimeNumbers] Modification of 2^p -1 +/- 2^n

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  • Robdine
    Peter 2^110503-1+2^100560 is prime! (M29) no need to stop testing at M28. gr. Rob ... From: Peter Lesala To: primenumbers@yahoogroups.com Sent: Friday,
    Message 1 of 2 , Oct 24, 2010
      Peter

      2^110503-1+2^100560 is prime! (M29)
      no need to stop testing at M28.

      gr. Rob


      ----- Original Message -----
      From: Peter Lesala
      To: primenumbers@yahoogroups.com
      Sent: Friday, October 22, 2010 7:34 PM
      Subject: [PrimeNumbers] Modification of 2^p -1 +/- 2^n



      In the last posting on this subject I showed how generation of primes can be done using the above formula. The generation of primes was successful up until the Mersenne pirme 2^86343 - 1. For the Mersenne after this it became difficult, and hence the reason I had to modify the formula.

      I am working on a document which explains all of the important steps. The document will be worth sharing if I succeed in the generation of primes of size 100 000 digits or more, which I am presently hunting.

      Below are the results showing PRPs and primes produced when applying the formula on 2^110503 - 1.

      A. 2^110503 - 2^n - 2^k - 1

      2^110503-2^1-2^2222-1 is probable prime! (a = 65413) (digits:33265)

      2^110503-2^1-2^2222-1 is probable prime! (verification : a = 65413) (digits:33265)

      2^110503-2^1-2^27322-1 is probable prime! (a = 48481) (digits:33265)

      2^110503-2^1-2^27322-1 is probable prime! (verification : a = 48481) (digits:33265)

      2^110503-2^80540-2^55077-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265)

      2^110503-2^80541-2^90960-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265)

      B. 2^110503 - 2^n - 2^k - 1

      2^110503+2^80541+2^66575-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265)

      2^110503+2^80541+2^80513-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265)

      2^110503+2^80541+2^96913-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265)

      C. 2^110503 - 2^n + 2^k - 1

      2^110503-2^80540+2^64940-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265)

      2^110503-2^80540+2^69229-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265)

      2^110503-2^80542+2^78335-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265)

      2^110503-2^80540+2^83148-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265)

      2^110503-2^80541+2^54527-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265)

      2^110503-2^80541+2^88273-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265)

      2^110503-2^80541+2^93763-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265)

      2^110503-2^80542+2^96299-1 is prime! [N+1, Brillhart-Lehmer-Selfridge] (digits:33265).

      The work is getting a bit more complicated. I had to jump values of n much greater than 1, for fast results. Thanks to the tips from David Broadhurst.

      Peter.

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