Mersenne Bibliography (original) (raw)
M. Mersenne
Cogitata Physico-Mathematica, Preface, Chapter XIX, 1644.
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
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
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
M107 is prime. Put into HTML by Conrad Curry.
R. E. Powers
Note on a Mersenne Number
BAMS
v. 40, 1934, p. 883
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
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
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
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
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
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
Put into HTML by Edward Brisse.
R. C. Archibald
Note 434[F]
MTAC
v. 2, 1947, p. 341
Put into HTML by Conrad Curry.
R. C. Archibald
Mersenne Numbers
Note 98
MTAC
v. 3, 1949, p. 398
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
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
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
Humorous history. Barker's "fiasco".
D. H. Lehmer
Recent Discoveries of Large Primes
Note 131
MTAC
v. 6, 1952, p. 61
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
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
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
Discovering the 13th through 17th Mersenne Primes.
H. Riesel
Mersenne Numbers
MTAC
v. 12, 1958, p. 207-213
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
Some corrections to above. Put into HTML by Conrad Curry.
A. Hurwitz
New Mersenne Primes
Math. Comp.
v. 16, 1962, p. 249-251
Discovery of 19th & 20th Mersenne primes.
J. L. Selfridge & A. Hurwitz
Fermat Numbers and Mersenne Numbers
Math. Comp.
v. 18, 1964, p. 146-148
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
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
Put into HTML by Conrad Curry.