Prime time (10)
An international team has just discovered a sequence of 10 consecutive prime numbers that are all equally spaced apart, like the rungs on a ladder — what mathematicians call an arithmetic progression, writes Keith Devlin.
This comes just a few weeks after the same team found an arithmetic progression of nine consecutive primes (The number of the beast, February 19).
At the time of the earlier discovery, team leader Harvey Dubner estimated that it could take six months of heavy duty computing to find 10 consecutive primes. They did it in less than two.
The team is made up of about a hundred people using a variety of PCs and workstations, connected together by the Internet. Team member Manfred Toplic of Klagenfurt, Austria, found nine consecutive primes in arithmetic progression on January 15. By an amazing coincidence, it was Toplic whose computer hit upon the new record breaking sequence of 10 consecutive primes.
The new sequence begins with the 93-digit number 100 99697 24697 14247 63778 66555 87969 84032 95093 24689 19004 18036 03417 75890 43417 03348 88215 90672 29719 and increases in steps of 210.
But Dubner believes the team may have reached the end of the road for many years to come. The mathematics used to write the computer program that found the records will not yield a sequence
of length 11 or more. The problem is that going up in steps of 210 will not work for more than 10 consecutive primes. The step will have to be at least 2310.
19 March 1998