Short Summaries of Articles about Mathematics
in the Popular Press
"The Scarcity of Cluster Primes," by Ivars Peterson. Science News, 6 February 1999, page 95.
To understand the distribution of all prime numbers, mathematicians often study the distribution of certain types of primes. One such type, the cluster primes, consists of those primes p with the property that "every even number less than p-2 must be the difference of two primes, both of which must be less than or equal to p." Recent calculations show that "by the time numbers reach 10 trillion, non-cluster primes outnumber cluster primes by a ratio of about 325 to 1." There are also results suggesting that cluster primes may be less numerous than certain other types of primes.
--- Kathryn Leonard