186 Jean-Marie De Koninck
11 305 (= 5 · 7 · 17 · 19)
the smallest pseudoprime in base 2 with four prime factors; if nk stands for
the smallest pseudoprime in base 2 having k prime factors, then n2 = 341,
n3 = 561, n4 = 11 305, n5 = 825 265, n6 = 45 593 065 and n7 = 370 851 481.
11 371
the smallest number n such that τ (n) τ (n + 1) . . . τ (n + 4): it is also
the smallest number n such that τ (n) τ (n + 1) . . . τ (n + 5): here
4 6 8 12 16 30 (see the number 61).
11 374 (= 2 · 112 · 47)
the 10
000th
composite number (see the number 133).
11 375
the largest solution n 109 of γ(n + 1) γ(n) = 19: the others are 98 and 135
(see the number 98).
11 447
the smallest prime factor of the Mersenne number 297 1, whose complete
factorization is given by
297
1 = 11447 · 13842607235828485645766393.
11 549
the 14th prime number pk such that p1p2 . . . pk + 1 is prime (see the number
379).
11 593
the first term of the smallest sequence of nine consecutive prime numbers all of
the form 4n + 1, namely 11 593, 11 597, 11 617, 11 621, 11 633, 11 657, 11 677,
11 681 and 11 689 (see the number 2 593).
11 605
the smallest number n such that τ (n) = τ (n + 1) = τ (n + 2) = τ (n + 3) =
τ (n + 4): the sequence of numbers satisfying this property begins as follows:
11605, 12855, 13782, 19142, 21494, 28374, 28375, 40311, 42805, 50585, . . . (see
the number 33).
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