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  • I'm scratching my head, because when I originally searched for the sequence on oeis some days ago, I did *not* get all the hits that I am now getting. Odd.
    mark.underwood@... Feb 16, 2014
  • Good find! And, your copy and paste looks accurate. From the AMS paper I see that starting at prime = 31 is a first occurrence where the least number solution is not prime. In that case, the least number solution is 307271 = 109 • 2819, and the least prime solution is 366791. Out of curiosity I decided to continue with my investigation past prime 19, up to prime 31, because I was...
    mark.underwood@... Feb 15, 2014
  • ...decompositions at all, and it seems to have no close competitors among other numbers of similar size. Jarek 2014-02-11 1:04 GMT+01:00 < mark.underwood@^$2.. > : Thanks Jarek, appreciated. Coming from the other direction, from the sum of two smooth numbers, I remain puzzled. I can...
    mark.underwood@... Feb 11, 2014
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  • ...smooth numbers that every small number is a sum of 2 such numbers if it is not somehow forbidden. Jarek 2014-02-10 18:41 GMT+01:00 < mark.underwood@^$2.. > : Given that a p-smooth number is a number with prime factors no greater than the prime p, 7 is the least number that can...
    mark.underwood@... Feb 10, 2014
  • Given that a p-smooth number is a number with prime factors no greater than the prime p, 7 is the least number that can't be written as the sum of two 2-smooth numbers. 23 is the least number that can't be written as the sum of two 3-smooth numbers. 71 is the least number that can't be written as the sum of two 5-smooth numbers Continuing we get the sequence 7, 23, 71, 311, 479...
    mark.underwood@... Feb 10, 2014
  • ---In primenumbers@^$1, wrote: Kevin Acres wrote: > Thanks for passing on Maximilian's observation. This was a sufficient > enough clue to enable completion of the puzzle in a very short time. I think that Kevin's correct answer, namely that the author is Michel Tremblay, will not spoil the mathematical puzzle. David I gave it a go. Discovering the 'base-10 procedure' was the easy...
    mark.underwood@... Jan 20, 2014
  • At least, my last two replies, sent in the last few days, have not been posted to the group for some reason. Odd.
    mark.underwood@... Nov 1, 2013
  • --- In primenumbers@^$1, "djbroadhurst" wrote: > > Here are the top 20, ranked by > P4 = sum(n=0,10^4,isprime(n^2+n+a)) > in the last column. I also give > P2 = sum(n=0,10^2,isprime(n^2+n+a)) > which is not always a reliable guide > to subsequent performance. > > rank a P2 P4 > [1, [ 247757, 71, 5028]] > [2, [ 595937, 61, 4978]] > [3, [ 1544987, 59, 4809]] > [4, [ 2640161, 61...
    Mark Jul 27, 2013
  • --- In primenumbers@^$1, Sebastian Martin Ruiz wrote: > > ________________________________ > > Prove: > > Theorem: > > Let c a positive even number >2 > > If (x,y)= (1,1) and (c^2/2-1,3c^2/2-2c-1) are the only positive integer solutions > > of the polynomial > > -3x^2+y^2-2xy-4cx+4cy+4=0 > > then c +1 and c-1 are twin primes > > > Sincerely > > Sebastián Martín Ruiz > Based on...
    Mark May 27, 2013
  • --- In primenumbers@^$1, Sebastian Martin Ruiz wrote: > > > Prove: > > Theorem: > > Let c a positive even number >2 > > If x=1 and y=1 is the only positive solution of the polynomial > > -3x^2+y^2-2xy-4cx+4cy+4=0 > > then c +1 and c-1 are twin primes > > Sincerely > > Sebastián Martín Ruiz > > [Non-text portions of this message have been removed] > Based on Warren's (corrected...
    Mark May 26, 2013