List of 38 Known Mersenne Primes,  2^p - 1

p =
2,
3,
5,
7,
13,
17,
19,
31 ( Euler, 1772),
61,
89,
107,
127 ( Lucas, 1876),
Edouard Lucas worked with Fibonacci numbers extensively in the last half of the 19th century (in fact it was Lucas who popularized the name "Fibonacci numbers"). He used properties of Fibonacci numbers to prove that the 39-digit Mersenne number 2^127 - 1 is prime.
521,
607,
1279,
2203,
2281,
3217,
4253,
4423,
9689,
9941,
11213,
19937,
21701 ( Curt Noll & Nickel, 1978),
23209,
44497,
86243 ( David Slowinski, 1982),
110503,
132049,
216091,
756839,
859433,
1257787,
1398269 (Joel Armengaud, Woltman, GIMPS, November 1996),
2976221 ( Gordon Spence, Woltman, GIMPS, August 24, 1997),
3021377 ( Roland Clarkson, Woltman, Kurowski, GIMPS, January 27, 1998, 6:43 pm PST) -- This number has 909,526 decimal digits
3021377 (Postscript Form)
6972593 ( Nayan Hajratwala, Woltman, Kurowski, GIMPS, June 1, 1999 -- This number has 2,098,960 decimal digits
BIG PRIME