Abstract: Ten consecutive primes in arithmetic progression

by Nikos Lygeros

 

Abstract: In 1967 the first set of 6 consecutive primes in arithmetic progres­sion was found. In 1995 the first set of 7 consecutive primes in arithmetic progression was found. Between November, 1997 and March, 1998, we suc­ceeded in finding sets of 8, 9 and 10 consecutive primes in arithmetic progres­sion. This was made possible because of the increase in computer capability and availability, and the ability to obtain computational help via the Internet. Although it is conjectured that there exist arbitrarily long sequences of con­secutive primes in arithmetic progression, it is very likely that 10 primes will remain the record for a long time.