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.
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