Those Fascinating Numbers 401
2216
+ 1
the
17th
Fermat number, a 19 729 digit number; it is a composite number,
whose smallest prime factor
825 753 601 = 1 575 ·
219
+ 1
was obtained by Selfridge in 1953;
the smallest counter example to the conjecture of F. Eisenstein (1823-1852)
according to which each number of the form
222·
··
2
+ 1
is prime: observe that the four smallest numbers of this form are 2 + 1 = 3,
22
+ 1 = 5,
222
+ 1 = 17 and
2222
+ 1 = 65537 (see the number 70 525 124 609).
286 243 1
the
28th
Mersenne prime, a 25 962 digit number.
244 496(244 497
1)
the
27th
even perfect number, a 26 790 digit number.
318 032 361 ·
2107 001
1
the first member of the largest known twin prime pair (Underbakke & Carmody,
2001): it is a 32 220 digit number.
2110 503 1
the
29th
Mersenne prime, a 33 265 digit number.
2217
+ 1
the
18th
Fermat number, a 39 457 digit number; it is composite and its smallest
prime factor,
31 065 037 602 817 = 59 251 857 ·
219
+ 1,
was found by Gostin in 1980 (see the number 70 525 124 609).
2132 049 1
the
30th
Mersenne prime, a 39 751 digit number.
Previous Page Next Page