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9006Re: Largest Ordinary Prime?

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  • paulunderwooduk
    Oct 1, 2002
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      --- Marcel Martin wrote:
      >
      > In a previous post, I wrote:
      > >>2^64695-2^15-1 19476 x43 2002 Unmentionable!
      >
      > >It could be archived as "3-bit prime".
      >
      > That's anywhat. I didn't take in account the minus signs :-))
      >

      Yes the signs are important for these trinomials. The most genral
      case I have is x^n+-x^k-1 (x,n,k all positive integers x>1,n>2,n>k>0
      and discounting Mersenne and "Fermat-type" (2^n+1) numbers. Call the
      trinomial f. I have not found a composite f:f|x^f-x. For instance
      this for f=x^3-x-1 passes 5 rounds of Miller Rabin at least for all
      x<19700000001 (1007728207 PrPs).

      I forgot to say in my previous post that Primo was used for proving
      the primailty of some of the factors of N+1. I used bc for my
      arithmetic ;)

      Paul
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