Thread: Dodecaproths
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Old 2006-01-14, 14:39   #6
Kosmaj's Avatar
Nov 2003

362210 Posts

Sometime before I thought to define ....proth ( what is the correct name for sixteen? )
I think it should be called HexadecaProth, and the next one if we ever encounter it is IcosaProth
It means 16 primes, but today to find such a pattern is impossible, even by a fast sieve and fast prp checking.
I don't think it's impossible! We have to find enough (i.e., many!) DodecaProths and one of them will surely be HexadecaProth. Check the following chain of 16 primes (the so-called bitwin with 7 links):
n=0,1,2,3,4,5,6,7; and "#" denotes primorial.
composed of 8 twins, and two Cunningham chains of first and second kind. Have you ever thought that such a chain exists? Only two such chains are currently known. The twin for n=0 has 23 digits. This is I think the place to look for HexadecaProths, around our exponent n=65 or 70.

If you can change your program to search for DodecaProths (ignoring of course potenital OctoProths whose "right legs" have small factors) I'll be willing to try!

Last fiddled with by Kosmaj on 2006-01-14 at 14:43
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