Those Fascinating Numbers 181

9 425

• the second number which can be written as the sum of two squares in six distinct

ways: 9 425 = 42 + 972 = 202 + 952 = 312 + 922 = 412 + 882 = 552 + 802 =

642 + 732 (see the number 5 525).

9 440

• the smallest number n such that each of the numbers n, n + 1, . . . , n + 20 is

divisible by one or several of the prime numbers p, with 2 ≤ p ≤ 13 (problem

taken in the 1986 USA and Canadian Olympiad: see Math. Mag. 59 (1986),

p. 309).

9 471

• the second number which is equal to the sum of the fourth powers of its dig-

its added to the product of its digits: the only other number satisfying this

property153 is 8 208.

9 474

• the largest number which can be written as the sum of the fourth powers of its

digits: 9 474 =

94

+

44

+

74

+

44;

the others are 1, 1 634 and 8 208.

9 511

• the smallest prime factor of the Mersenne number

2317

− 1, whose complete

factorization is given by

2317

− 1 = 9511 · 587492521482839879 · 4868122671322098041565641

·9815639231755686605031317440031161584572466128599.

9 531

• the 18th number n such that n · 2n − 1 is prime (see the number 115).

9 551

• the 12th and largest known prime number p such that (3p − 1)/2 is itself a

prime number (see the number 1 091).

153One can argue, as in the footnote tied to the number 1 324, that any such number can have at

most six digits; using a computer, it is then easy to prove that 9 471 is the largest number with this

property.