This is Dataplot data file PRIMESM.DAT The exponent forming the first 30 Mersenne Prime Numbers Definition--The set of Mersenne prime numbers is that subset of prime numbers of the form 2**p - 1 where p itself is some prime number. Note-- first Mersenne prime number : 2**2 - 1 = 3 which is prime second Mersenne prime number : 2**3 - 1 = 7 which is prime third Mersenne prime number : 2**5 - 1 = 31 which is prime fourth Mersenne prime number : 2**7 - 1 = 127 which is prime fifth Mersenne prime number : not 2**11 - 1 = 2047 since not prime fifth Mersenne prime number : 2**13 - 1 = 8191 which is prime Number of observations = 30 ? Number of observations per line image = 2 Order of observations per line image-- 1. Response variable = p such that M = 2**p - 1 2. Factor 1 = dummy index (1 to 31) Reference--Science News, Feb. 6, 1988, page 85. Reference--Schroeder, Manfred R. (1983). Where is the Next Mersenne Prime Hiding? The Mathematics Intelligencer. Vol. 5, No. 3. Of Interest--The plot of log2(y) versus X has slope close to e**(-gamma) where gamma = Euler's constant (.577216...) and e = 2.718... and e**(-gamma) = .561460... exponent p index ----------------------- 2 1 3 2 5 3 7 4 13 5 17 6 19 7 31 8 61 9 89 10 107 11 127 12 521 13 607 14 1279 15 2203 16 2281 17 3217 18 4253 19 4423 20 9689 21 9941 22 11213 23 19937 24 21701 25 23209 26 44497 27 86243 28 110503 29 216091 30