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  • The following value resolves a question implicitly raised in Prime Curios!: 4 Prime Curios!: 4 Chris K. Caldwell One of many pages of prime number curiosities and trivia. This page discusses 4 Come explore a new prim... 25658391953833 I'm bringing it to the attention of this group a) as an ordinary report, and b) because the next term of the implied sequence is probably within...
    James Merickel Jul 1
  • Found two cases, so far, with total 15 digits and one with total 16 -- of 24/48 primes. Nothing better than 21/44 (my stupid mistake was thinking I made one earlier -- in mathematical reasoning at least (meaning my cojecture collapsed, of course), if you've been following) among cases of 4, 8 or 12 repeats (not close for 12, done more than exhaustively (challenge is to find even 12...
    James Merickel Jun 3
  • Another: {(197837, 738791), (705247, 742507), (764969, 969467)} also gives 24/48 primes. If there isn't one producing 25, then I'll not report on this again until searching something else beyond this cohort is completed (No report of a 4th trio of pairs if there is one). The basis for the initial conjecture was a bit light, but the search did go pretty far in before any collection...
    James Merickel May 8
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  • Out in the last hour, I have a new trio with the same count of 24 primes; so something closer to a conjecture than guess than the original, with considerably more of the search completed, is to include {(105097, 790501), (339887, 788933), (711839, 938117)}. This part of the search shouldn't be very long to completion, but only a restricted search for total digits of concatenation...
    James Merickel May 6
  • In my recent lengthy heuristics post I promised a sharp heuristic approximation. I decided this was merely excess work for myself and would enlighten few if any here. I did post a table of the simpler approximation for 3-17 digits. For small numbers of digits there is an inaccuracy in the approach (but I won't go into it; if the reader doesn't see it immediately I apologize for not...
    James Merickel May 1
  • [Note: The last part I state as being here will be submitted later. Tired (very), and it's not that much on point anyway.] I decided to continue, partly because I had a temporary thought that my parenthetical problem on triples might be impossible (the candidate count is exponential in the number of digits N, however; and the count of satisfactory triples is O((10^N)/(N^14...
    James Merickel Apr 27
  • ...the pair of larger and smaller. This would certainly be HARD, in comparison). ----- Forwarded Message ----- From: James Merickel moralforce120@^$1 [primenumbers] To: Yahoogroups Sent: Thu Apr 13 2017 09:43:01 GMT-0400 (Eastern Standard Time) Subject: [PrimeNumbers] heuristics...
    James Merickel Apr 26
  • Done. No interest now in finding larger terms. Just lucky it's small: There are problems with the heuristics, but they're tiny for 13-digit numbers as far as I can see (I get further multipliers of 1.215 and 2.650 for 14- and 15-digit numbers, considering factors of 10^i + 1). JGM
    James Merickel Apr 15
  • Still researching the same thing, but my original results were closer to correct (not sure why). Here's the PARI program for 10- to 19-digit heuristically expected counts: for(i=10,19, if(i%2,k=7,k=3); C= (16*10^(i-2)/3)*((15/(4*(i-.3)*log(10)))^3)*.5*1.21* ((15/(4*(2*i-.3)*log(10)))^8); print1(i":"C*1.1^k"\n")) Results for 10 to 12 digits are expected counts (equivalent for all...
    James Merickel Apr 13
  • I'm told heavier resources are on it already. [Was dedicating my new i7 laptop to increasing the bound on the next Smarandache-Wellin prime (2357-type w/o truncation of end primes); but just checked that bound, and IF I'm going to do that I need to start higher (at a million as of 2015)] JGM
    James Merickel Apr 11