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. |