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131.—RECENT
DISCOVERIES OF
LARGE PRIMES.
Ever since LUCAS announced the discovery
of the prime
2
127
- 1 in
1876, many attempts have been made to discover larger primes. These
attempts have succeeded only recently as follows:
(a) A. FERRIER
1
has identified
(2
148
+ )/17
as a prime, using a method based on the converse of Fermat's theorem
and a desk calculator.
(b) Using the same method and the EDSAC, WHEELER
and MILLER
2,3
have proved the primality of
1 + k(2
127
- 1)
for k = 114, 124, 388, 408, 498, 696, 738, 744, 780, 934, 978,
and finally
1 + 180(2
127
- 1)
2
,
a number of 79 decimal digits.
(c) Using the standard LUCAS test for Mersenne
primes as programmed by R. M. ROBINSON,
the SWAC has discovered the primes
2
521
- 1 and
2
607
- 1 on
January 30, 1952. These lead to the 13th and 14th perfect numbers.
1 Letter
of July 14, 1951.
2 J. C. P.
MILLER & D. J. WHEELER,
"Large prime numbers," Nature, v. 168, 1951,
p. 838.
3 J. C. P.
MILLER,
"Large primes," Eureka, 1951,
no. 14, p. 10-11.
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