23. A NEW RESULT CONCERNING A MERSENNE NUMBER.—In Scripta Mathematica, v. 3, 1935, p. 112-119, there is an article by R. C. ARCHIBALD on "Mersenne's numbers," M p = 2 p  - 1, (p prime). This article tabulates all results known in 1935 (except one) for these numbers p = 2 to p = 257. Archibald has pointed out that the one result he had overlooked was that announced by POWERS in London Math. So., Proc., v. 12, Mar. 13, 1913, p. iii, that 2 257  - 1 has no factor < 10,017,000. Until recently it was not known whether 6 of the 55 Mersenne numbers were prime or composite. On August 11, 1944, I completed the proof that the smallest of these 6 numbers, M 157 , is composite. Details concerning my computations are about to appear in Nat. Acad. Sci., Proc. Our present knowledge of the M p is tabulated below.

p Character of M p
2,3,5,7,13,17,19,31,61,89,107,127 Prime
11,23,29,37,41,43,47,53,59,67,71,73,79 Completely factored
113,151,179,223,233,239,251 Incompletely factored but two or more prime factors known
83,97,131,163,173,181,191,197,211 Only one prime factor known
101,103,109,137,139,149,157,241,257 Composite but no prime factor known
167,193,199,227,229 Character unknown
H. S. UHLER
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