Accession Number : AD0429868


Title :   THREE NEW MERSENNE PRIMES, AND A CONJECTURE,


Corporate Author : ILLINOIS UNIV URBANA DIGITAL COMPUTER LAB


Personal Author(s) : Gillies,Donald B


Report Date : 27 May 1963


Pagination or Media Count : 29


Abstract : The Mersenne primes, 9689, 9941, and 11213, are discussed and the following conjecture is formulated: If A is less than or equal to B is less than or equal to the square root of Mp (where A and B are integers and Mp is a Mersenne prime), then the probability that there is no divisor s of Mp in the interval (A,B), is given asymptotically by logA/Log B if A is greater than or equal to 2p. or by log2p/logB if A is less than 2p; and prime divisors are statistically inde pendent. Thus Mersenne numbers are asserted to have the same likelihood of being prime, and to have the same statistical distribution of factors as integers of about the same size which are selected to have no factors less that 2p but are otherwise randomly chosen. (Author)


Descriptors :   *NUMBER THEORY , COMPUTER PROGRAMMING , STATISTICAL DISTRIBUTIONS


Distribution Statement : APPROVED FOR PUBLIC RELEASE