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Re: [PrimeNumbers] Digest Number 638

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  • Dick Boland
    Hello, ... No, But!, I did look at 2^n*n#-1 and have assembled my fragments. They have a good, neat looking form, but the form is also flawed. For non-prime n,
    Message 1 of 1 , Aug 2, 2002
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      Hello,

      > Did anybody look for primes of the form p#^2^n+1
      > (or n!^2^n+1)? E.g., 1801#^16+1 is prime.

      No, But!,
      I did look at 2^n*n#-1 and have assembled my
      fragments.
      They have a good, neat looking form, but the form is
      also flawed. For non-prime n, "proper" notation
      would be 2^n*P(pi(n))#-1, ruining the repeating digits
      effect in the presentation. When n is prime, the
      notational collapse doesn't exist, so whatever these
      primes should be called, n has to be prime for it to
      be a perfect "whatever...".

      There can be circumstances where taking the primorial
      of n=composite can create several instances of the
      same
      number in an iterated run. With this form, the
      multipler 2^n ensures each is distinct.
      Thus, is it flawful, lawful, awful to say
      2^16*16#-1 is prime?

      Here's what I have found on these,
      any one wants to take it farther,
      be my guest.

      -Dick

      After n=16, they are all PRP's.
      I never got around to testing them.

      2^2*2#-1 is prime!
      2^3*3#-1 is prime!
      2^7*7#-1 is prime!
      2^8*8#-1 is prime!
      2^14*14#-1 is prime!
      2^16*16#-1 is prime!
      2^18*18#-1
      2^20*20#-1
      2^40*40#-1
      2^42*42#-1
      2^44*44#-1
      2^53*53#-1
      2^134*134#-1
      2^154*154#-1
      2^185*185#-1
      2^187*187#-1
      2^191*191#-1
      2^197*197#-1
      2^200*200#-1
      2^201*201#-1
      2^230*230#-1
      2^235*235#-1
      2^239*239#-1
      2^244*244#-1
      2^256*256#-1
      2^282*282#-1
      2^303*303#-1
      2^358*358#-1
      2^489*489#-1
      2^536*536#-1
      2^665*665#-1
      2^684*684#-1
      2^719*719#-1
      2^1098*1098#-1
      2^1204*1204#-1
      2^1400*1400#-1
      2^1516*1516#-1
      2^1629*1629#-1
      2^1903*1903#-1
      2^1997*1997#-1
      2^1999*1999#-1
      2^2104*2104#-1
      2^2477*2477#-1
      2^3075*3075#-1
      2^3676*3676#-1
      2^3785*3785#-1
      2^4115*4115#-1
      2^5429*5429#-1
      2^5808*5808#-1
      2^6069*6069#-1
      2^6276*6276#-1
      2^9095*9095#-1
      2^10423*10423#-1
      2^10839*10839#-1
      2^16181*16181#-1
      2^17521*17521#-1
      2^17734*17734#-1
      2^20451*20451#-1
      2^22560*22560#-1
      2^29545*29545#-1
      2^30069*30069#-1
      2^33389*33389#-1
      ** Run Stopped at 34952

      Here's the largest cofactor PRP's in the run
      (2^12804*12804#-1)/15959
      (2^15233*15233#-1)/263089
      (2^18932*18932#-1)/116981
      (2^27766*27766#-1)/1993067

      And here are the caps of a couple Sophie Germains,
      (no more of these at least to n=918).
      2^(53-1)*53#-1 (digits:36 checksum:_8F526EDE_)
      2^(201-1)*201#-1 (digits:143 checksum:_E1E2C9AF_)



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