Thread: Largest Simultaneous Primes View Single Post
 2006-02-04, 14:33 #2 Kosmaj     Nov 2003 2·1,811 Posts After several attempts (over half an hour) I was able to open his page. The current records are (using i-th prime for our multi-Proths): 8-primes: 206 digits (tuplet), Octoproth (n=346): 105 digits 12-primes: 44 digits (bitwin), Dodecaproth (n=91): 28 digits 16-primes: 26 digits (tuplet), Hexadecaproth (if we find one for n=76): 24 digits The hendicap of using the i-th prime (among 2i primes) is not a big problem for Octoproths but it is for Hexadecaproths. For example, let's suppose we find a Hexadecaproth for n=76 and a 17-digit k. Then, we'll have 2 primes with 23 digits, 6 primes with 24 digits and 8 primes with 39-41 digits which I think (obviously?) is better than 16 primes with 26 digits, but based on 8-th prime with 24 digits our Hexadecaproth will be ranked below the 26-digit tuplet. Another possible size measure I was thinking about is a "score" used by prof. Caldwell on Top-5000 (or a variation of it) summed over all primes in the group. In any case approaching existing record in any catogery (4, 8, 12) will require a huge computation effort which presently I'm not ready to undertake. Finally, I don't have a problem accepting his second condition, k<2^(n-1), since we begin the search from k=1, not from k=2^n-1, and thus all our large multi-Proths satisfy the condition. Last fiddled with by Kosmaj on 2006-02-04 at 14:35