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16564Re: [PrimeNumbers] Infinite Number of Twin Primes

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  • Jacques Tramu
    May 6, 2005
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      How many fact-twins are there ?

      A pair of fact-twins are twins primes (ft, ft+2) if exists n such as
      ft = n! + p, where p and p+2 are twin primes;

      The following table count the number of fact-twins in intervals of length
      10^9 starting at
      0, up to 10^18.

      pi = number of primes in the interval [from, from+10^9]
      twins = number of twins
      fact-twins : number of fact-twins
      % = fact-twins * 100 / twins

      from pi twins fact-twins
      %
      1 50847534 3424506 999836 29,20%
      10^9 47374753 2963535 815419 27,51%
      10^10 43336106 2477174 674611 27,23%
      10^11 39475591 2055627 547106 26,62%
      10^12 36190991 1730012 386360 22,33%
      10^13 33405006 1473196 318563 21,62%
      10^14 31019409 1270499 265221 20,88%
      10^15 28946421 1105560 225366 20,38%
      10^16 27153205 972510 194566 20,01%
      10^17 25549226 861742 153809 17,85%
      10^18 24127085 769103 135977 17,68%
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