Mersenne Bibliography

This page provides a number of published resources about Mersenne numbers, largely based off work Luke Welsh did to gather these in the late 1990s. Contents are in chronological order.

Author Resource Links Notes
M. Mersenne Cogitata Physico-Mathematica, Preface, Chapter XIX, 1644. HTML

Mersenne wrote in Latin, in 1644.

In 1878, Lucas's paper was published (in French) in the American Journal of Mathematics. One page, quoting Mersenne, was in Latin.

In 1969, Kravitz translated (with corrections) the first 47 pages of Lucas' text in the AJM (pp. 184-240). Mersenne's Latin was also translated into English, as presented here.

Kravitz's English text, published in the Fibonacci Quarterly, was paginated from 1 to 77.

In March, 1997, Edward Brisse discovered Kravitz's paper and ported it to HTML. Kravitz's footnotes were faithfully reproduced at the bottom of each "page".

Edward also deserves the credit for obtaining the necessary permission from the Fibonacci Association.

Conrad Curry (March, 1997) did further HTML work, including the clever migration of Kravitz's footnotes to a sidebar and the addition of new footnotes quoting Dickson (bottom).

É. Lucas Récréations Mathématiques,
Paris Gauthier-Villars (1883), tome II, Note II, Sur les nombres de Fermat et de Mersenne, p.230-235
HTML (French) HTML (English) Put into HTML by Edward Brisse. English translation by Edward Brisse and Joseph E. Houle.
R. E. Powers The Tenth Perfect Number
Amer. Math. Monthly
v. XVIII, no. 11, Nov. 1911, p. 195-197
Plain Text M89 is prime. First proof that Mersenne was wrong.
R. E. Powers On Mersenne's Numbers
P. London Math. Soc.
Record of preceedings at meetings
s. 2, v. 13, 1914, p. xxxix
HTML M107 is prime. Put into HTML by Conrad Curry.
R. E. Powers Note on a Mersenne Number
BAMS
v. 40, 1934, p. 883
HTML M241 is composite.
D. H. Lehmer On Lucas's Test for the Primality of Mersenne's Numbers
J. London Math. Soc.
v. 10, 1935, p. 162-165
HTML Wanted List: M157, M167, M193, M199, M227, and M229. Put into HTML by Conrad Curry.
R. C. Archibald Mersenne's Numbers
Scripta Mathematica
v. 3, 1935, p. 112-119
HTML A great history. Mersenne predicted M131071. Put into HTML by Conrad Curry.
H. S. Uhler Notes
#23 A New Result Concerning a Mersenne Number
MTAC
v. 1, 1944, p. 333
HTML M157 is composite. Put into HTML by Conrad Curry.
H. S. Uhler Notes
#33 A New Result Concerning a Mersenne Number
MTAC
v. 1, 1944, p. 404
HTML M167 is composite. Put into HTML by Conrad Curry.
H. S. Uhler Queries--Replies
#55 A New Result Concerning a Mersenne Number
MTAC
v. 2, 1945, p. 94
HTML M229 is composite. Put into HTML by Conrad Curry.
J. Ferrier Les nombres premiers,
Paris Vuibert (1947), Chapitre IX, Les nombres de Mersenne, p.40-41
HTML (French) HTML (English) Put into HTML by Edward Brisse.
R. C. Archibald Note 434[F]
MTAC
v. 2, 1947, p. 341
HTML Put into HTML by Conrad Curry.
R. C. Archibald Mersenne Numbers
Note 98
MTAC
v. 3, 1949, p. 398
HTML On all 55 original Mersenne Numbers. Put into HTML by Conrad Curry.
J. C. P. Miller
D. J. Wheeler
Large Prime Numbers
Nature
v. 168, (1951), p. 838
HTML The dawn of the computer age. Edsac computer breaks Lucas's record.
J. C. P. Miller Large Primes
Eureka
no. 14, (1951), p. 10, 11
Plain Text How the Edsac set the record announced above.
H. S. Uhler A Brief History of the Investigations on Mersenne's Numbers and the Latest Immense Primes
Scripta Mathematica
v. 18, 1952, p. 122-131
HTML Humorous history. Barker's "fiasco".
D. H. Lehmer Recent Discoveries of Large Primes
Note 131
MTAC
v. 6, 1952, p. 61
HTML Announces Discovery of 13th & 14th Mersenne Primes, M521 & M607. Put into HTML by Conrad Curry.
D. H. Lehmer A New Mersenne Prime
Note 138
MTAC
v. 6, 1952, p. 205
HTML Announces Discovery of 15th Mersenne Prime, M1279. Put into HTML by Conrad Curry.
D. H. Lehmer Two New Mersenne Primes
Note 146
MTAC
v. 7, 1953, p. 72
HTML Announces Discovery of 16th & 17th Mersenne Primes, M2203 & M2281. Put into HTML by Conrad Curry.
R. M. Robinson Mersenne and Fermat Numbers
PAMS
v. 5, 1954, p. 842-846
HTML Discovering the 13th through 17th Mersenne Primes.
H. Riesel Mersenne Numbers
MTAC
v. 12, 1958, p. 207-213
HTML Discovery of 18th Mersenne Prime: M3217. Some factors in error - see below. Put into HTML by Conrad Curry.
J. L. Selfridge MTE 271
MTAC
v. 13, 1959, p. 142
HTML Some corrections to above. Put into HTML by Conrad Curry.
A. Hurwitz New Mersenne Primes
Math. Comp.
v. 16, 1962, p. 249-251
HTML Discovery of 19th & 20th Mersenne primes.
J. L. Selfridge & A. Hurwitz Fermat Numbers and Mersenne Numbers
Math. Comp.
v. 18, 1964, p. 146-148
HTML Residues for 5000 < p < 6000. Put into HTML by Conrad Curry.
S. Kravitz & M. Berg Lucas's Test for Mersenne Numbers, 6000 < p < 7000
Math. Comp.
v. 18, 1964, p. 148-9, MR28#1152
HTML Residues for 6000 < p < 7000. Put into HTML by Conrad Curry.
D. Shanks & S. Kravitz On the Distribution of Mersenne Divisors
Math. Comp.
v. 21, 1967, p. 97-101
HTML Put into HTML by Conrad Curry.
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