402 Jean-Marie De Koninck

11 . . . 1

49 081

• the sixth prime number whose digits are only 1’s (see the number 19).

286 242(286 243 − 1)

• the 28th even perfect number, a 51 924 digit number.

2216 091

− 1

• the

31rst

Mersenne prime, a 65 050 digit number.

2110 502(2110 503

− 1)

• the 29th even perfect number, a 66 530 digit number.

2218

+ 1

• the

19th

Fermat number, a 78 914 digit number; it is composite and its smallest

prime factor, discovered by Western in 1903, is 5 242 881 = 5 ·

220

+ 1 (see the

number 70 525 124 609).

262 419 · 2262 419 + 1

• the largest known Cullen prime number, a 79 002 digit number (Darren Smith,

1998) (see the number 141).

2132 048(2132 049

− 1)

• the 30th even perfect number, a 79 502 digit number.

11 . . . 1

86 453

• the seventh prime number whose digits are only 1’s (see the number 19).

3 ·

2303 093

+ 1

• the largest known prime of the form k ·

2n

+ 1, a 91 241 digit number (Jeffrey

Young,

1998).214

214These

numbers are very useful in the search for prime factors of Fermat numbers, because it is

well known (since Euler) that each prime factor of

22m

+ 1 is of the form k · 2m+2 + 1.