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).
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