Large Prime Numbers
   For about seventy-five years the largest known prime number has been P = 2127 - 1, identified as such by Edouard Lucas. It has remained the largest known in spite of many attempts to identify larger ones, although there have been conjectures and claims insufficiently substantiated or entirely unproved.
   Recently we have prepared a routine for testing on the Edsac the primality of numbers of the form kP + 1, with P as defined above, and have found ten values of k that give prime numbers. The largest of these gives the present (June 7) largest known prime, namely,
934(2127 - 1) + 1

June 7.
J. C. P. MILLER
D. J. WHEELER
   Note added in proof (October 8). Further work on the Edsac by Wheeler and myself has demonstrated the primality of
978(2127 - 1) + 1
and culminated in early July in the identification of the present largest known prime,
180(2127 - 1 )2 + 1.
   Also, in early July, A. Ferrier, of France, using a desk machine, demonstrated the primality of
(2148 + 1)/17,
which is the second largest known prime.
J. C. P. MILLER
University Mathematical Laboratory,
Cambridge.

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