An interesting tidbit from the Number Theory List. Of course, the average spacing between primes must be logN, from the prime number theorem. I don't know anything about the variance of the spacing: Is it poisson?, How unusual is a 10x normal gap? The first gap of 100 is around 10^6, making a 7x gap. I think Shanks posed the question "Where do we expect to find the first gap of 1M?" Rich rcs@cs.arizona.edu --------- Date: Thu, 15 Jan 2004 20:56:07 -0500 From: Jens Kruse Andersen <jens.k.a@get2net.dk> Subject: A prime gap of 1001548 To: NMBRTHRY@LISTSERV.NODAK.EDU Hans Rosenthal and I have found a prime gap of 1001548 between two probabilistic primes (prp's) with 43429 digits. Sieving for small factors used the GMP multiple precision library, and prp testing of the remaining numbers was performed by the program PrimeForm/GW. The logarithm of the primes is 99997 so the gap is 10.02 times the "typical" gap by the prime number theorem. I think that regardless of relative size, this is the first known prime "megagap" with identified (probabilistic) primes as gap ends. The primes have no simple expression. See more details at http://hjem.get2net.dk/jka/math/primegaps/megagap.htm -- Jens Kruse Andersen