Those Fascinating Numbers 397

was obtained by Selfridge in 1953, while the factor

6 487 031 809 = 395 937 ·

214

+ 1,

was obtained by Brillhart in 1962 (see the number 70 525 124 609).

2520(2521

− 1)

• the 13th even perfect number, a 314 digit number.

11 . . . 1

317

• the fourth prime number all of whose digits are 1 (see the number 19).

2606(2607

− 1)

• the

14th

even perfect number, a 366 digit number.

21 279 − 1

• the

15th

Mersenne prime, a 386 digit number.

2211

+ 1

• the 12th Fermat number, a 617 digit number; it is a composite number, for

which two of its prime factors, namely

319 489 = 39 ·

213

+ 1 and 974 849 = 119 ·

213

+ 1,

were obtained by Cunningham in 1899 (see the number 70 525 124 609).

22 203

− 1

• the 16th Mersenne prime, a 664 digit number.

22 281

− 1

• the

17th

Mersenne prime, a 687 digit number.

21 278(21 279

− 1)

• the 15th even perfect number, a 770 digit number.