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