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).