Those Fascinating Numbers 217

43 331

• the smallest prime number p such that p + 60 is prime and such that each

number between p and p + 60 is composite (see the number 139).

43 441

• the smallest prime factor of the Mersenne number

2181

− 1, whose complete

factorization is given by

2181

−1 = 43441·1164193·7648337·7923871097285295625344647665764672671.

43 875

• the ninth odd number n 1 such that γ(n)|σ(n) (see the number 135).

44 360

• the smallest number n such that ω(n) = ω(n + 1) = . . . = ω(n + 8), the

common value being 3; if nk stands for the smallest number n such that ω(n) =

ω(n + 1) = . . . = ω(n + k − 1), then n1 = n2 = n3 = n4 = 2, n5 = 54, n6 = 91,

n7 = n8 = 141, n9 = 44 360, n10 = 48 919, n11 = 218 972, n12 = n13 = n14 =

526 095, n15 = 17 233 173 and n16 = 127 890 362; for the analogue question with

the function Ω(n), see the number 602.

44 484

• the second number n such that ω(n) = ω(n+1) = ω(n+2) = 4 (see the number

37 960).

44 497

• the exponent of the 27th Mersenne prime 244 497 − 1 (Nelson and Slowinski,

1979).

44 507

• the 40th Lucas prime number (see the number 613).

44 706

• the number of Carmichael numbers

1014

(see the number 646).