After several attempts (over half an hour) I was able to open his page. The current records are (using ith prime for our multiProths):
8primes: 206 digits (tuplet), Octoproth (n=346): 105 digits
12primes: 44 digits (bitwin), Dodecaproth (n=91): 28 digits
16primes: 26 digits (tuplet), Hexadecaproth (if we find one for n=76): 24 digits
The hendicap of using the ith 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 17digit k. Then, we'll have 2 primes with 23 digits, 6 primes with 24 digits and 8 primes with 3941 digits which I think (obviously?) is better than 16 primes with 26 digits, but based on 8th prime with 24 digits our Hexadecaproth will be ranked below the 26digit tuplet.
Another possible size measure I was thinking about is a "score" used by prof. Caldwell on Top5000 (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^(n1), since we begin the search from k=1, not from k=2^n1, and thus all our large multiProths satisfy the condition.
Last fiddled with by Kosmaj on 20060204 at 14:35
