312 Jean-Marie De Koninck
43 112 609
the exponent of the 46th known Mersenne prime 243 112 609 −1 (a 12 978 189 digit
number) discovered by Edson Smith in September 2008, using the programme
developed by G. Woltman (see the number 1 398 269)193.
43 570 803
the smallest number n such that φ(n), φ(n + 1), φ(n + 2), φ(n + 3), φ(n + 4)
and φ(n + 5) have the same prime factors, namely here the primes 2, 3, 5, 7,
13 and 19 (see the number 266 401; see also the number 3 777 for the analogue
problem for the σ(n) function).
45 086 079
the number of nine digit prime numbers (see the number 21).
45 326 160
the fifth number n such that φ(n) + σ(n) = 4n (see the number 23 760).
45 532 800 (=
27
·
33
·
52
· 17 · 31)
the fifth 4-perfect number (see the number 30 240): Carmichael proved that it
is the largest 4-perfect number with exactly five distinct prime factors.
45 581 759
the
11th
solution of σ2(n) = σ2(n + 2) (see the number 1 079).
45 592 577
the smallest prime factor of F10 =
2210
+ 1, whose complete factorization is
given by
F10 = 45592577 · 6487031809
·4659775785220018543264560743076778192897 · P252.
45 593 065 (=5 · 7 · 17 · 19 · 37 · 109)
the smallest pseudoprime in base 2 having exactly six prime factors (see the
number 11 305).
193Officially, the discoverer received a 100 000$ reward. A 150 000$ prize will be awarded for the
discovery of a 100 million digit prime number; and we might have to wait some time before someone
wins the 250 000$ prize for the discovery of a billion digit prime number.
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