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Chen prime with 70301 digits

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  • Jens Kruse Andersen
    PrimeForm e-group has found the largest known Chen prime: (1284991359*2^98305+1)*(96060285*2^135170+1)-2 2^98305 divides N+1 which enables a BLS proof: D: pfgw
    Message 1 of 3 , Oct 7, 2005
      PrimeForm e-group has found the largest known Chen prime:
      (1284991359*2^98305+1)*(96060285*2^135170+1)-2

      2^98305 divides N+1 which enables a BLS proof:

      D:>pfgw -tp -q"(1284991359*2^98305+1)*(96060285*2^135170+1)-2"
      PFGW Version 1.2.0 for Windows [FFT v23.8]

      Primality testing (1284991359*2^98305+1)*(96060285*2^135170+1)-2
      [N+1, Brillhart-Lehmer-Selfridge]
      Running N+1 test using discriminant 5, base 1+sqrt(5)
      Calling Brillhart-Lehmer-Selfridge with factored part 42.10%
      (1284991359*2^98305+1)*(96060285*2^135170+1)-2 is prime!
      (6253.7959s+0.0222s)

      Congratulations to Micha Fleuren who got the hit after bad e-group luck,
      some of it on larger candidates.
      The other PRP testers were Jens Kruse Andersen, Pierre Cami, Jason Earls,
      Andy Klingeleers, Paul Underwood, Thomas Wolter.
      PrimeForm/GW performed the PRP tests.
      Phil Carmody made chenpq2 which trial factored to 2^31.
      Thanks to all participants.

      Also thanks to Chris Caldwell for maintaining the Prime Pages database.
      Without it we might not have resources to find a BLS provable Chen.
      The database says:
      1284991359*2^98305+1, David Underbakke and Phil Carmody in 2001.
      96060285*2^135170+1, David Underbakke with Yves Gallot's Proth.exe in 2002.

      3 coincidences (maybe not big if the database is examined):
      The same person (Underbakke) found both primes.
      Phil Carmody who wrote the Chen sieve also contributed to one of them.
      Both primes were found in old twin searches and now they combine to
      beat the current twin record as largest known Chen.

      Paul: I will suggest a bio text later.
      Micha: You can submit with credit to PrimeForm and egroup.
      You can try adding the comment Chen and see whether Chris tolerates it.

      In the weekend I will mail MathWorld with a suggested article on Chen primes.
      Guess whether the record will be mentioned ;-)
      I will also submit it to http://en.wikipedia.org/wiki/Chen_prime

      --
      Jens Kruse Andersen
    • Paul Underwood
      ... Great! I have stopped my part in the Chen search -- more elbow grease for 321search . I had put many computing cycles into this Chen project and I pleased
      Message 2 of 3 , Oct 7, 2005
        >
        > PrimeForm e-group has found the largest known Chen prime:
        > (1284991359*2^98305+1)*(96060285*2^135170+1)-2

        Great! I have stopped my part in the Chen search -- more elbow grease
        for "321search".

        I had put many computing cycles into this Chen project and I pleased
        that we've found something at last.

        Maybe, a big CGH proven prime would be nice ;-)

        Paul
      • Pierre CAMI
        Great hunting as the no twin chen primes are near as exceptional than the twin primes Here my count of the ratio R=Sc/St with Sc no twin chen primes and St
        Message 3 of 3 , Oct 7, 2005
          Great hunting as the "no twin" chen primes are near as exceptional
          than the twin primes
          Here my count of the ratio R=Sc/St with Sc "no twin" chen primes
          and St twin primes (count one for a pair of twin)

          N R
          N=10*10^6 2,8256
          N=20*10^6 2,8814
          N=40*10^6 2,9360
          N=50*10^6 2,9544
          N=60*10^6 2,9689
          N=70*10^6 2,9791
          N=80*10^6 2,9911
          N=90*10^6 2,9975
          N=100*10^6 3,0030
          N=120*10^6 3,0148
          N=140*10^6 3,0222
          N=160*10^6 3,0319
          N=180*10^6 3,0416
          N=200*10^6 3,0472
          N=240*10^6 3,0596
          N=280*10^6 3,0683
          N=320*10^6 3,0744
          N=360*10^6 3,0816
          N=400*10^6 3,0872

          Remarks that R seems to tends to Pi (3.14159...) as N increases !!!

          about 3 to 4 "no twin" chen primes for a pair of twin

          I stop now my hunt on chen , congratulations for the great hunt

          Pierre
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