342 Jean-Marie De Koninck
2 027 651 281
the number used by Fermat to illustrate the factorization method which bears
his name:
2 027 651 281 = (45 041 + 1 020)(45 041 1 020) = 46 061 · 44 021.
2 037 968 761
the 100 000 000th prime power, in fact here a prime number (see the number
419).
2 038 074 743
the 100 000
000th
prime number (see the number 541).
2 071 761 216
the smallest number n such that β∗(n) = β∗(n + 1) = β∗(n + 2) = β∗(n + 3):
here the common value is 31, since
2 071 761 216 =
26
· 3 · 7 · 19 · 81131 −→ β∗(n) = 31,
2 071 761 217 = 31 · 66831007 −→ β∗(n + 1) = 31,
2 071 761 218 = 2 · 29 · 35720021 −→ β∗(n + 2) = 31,
2 071 761 219 =
34
· 11 · 17 · 136777 −→ β∗(n + 3) = 31;
the sequence of numbers satisfying this property begins as follows: 2071761216,
2242927773, 3038038626, 3757781352, 4450857765, 4920655947, 7341730097,
8236135395, 8489884267, . . .
2 090 188 800
the fourth number which is equal to the product of the factorials of its digits in
base 12: 2 090 188 800 = [4, 10, 4, 0, 0, 0, 0, 0, 0]12 = 4! · 10! · 4! · 0! · 0! · 0! · 0! · 0! · 0!
(see the number 21 772 800).
2 147 483 647
the eighth Mersenne prime: 2 147 483 647 = 231 1.
2 200 079 025 (=
32
·
52
·
532
·
592)
the 100 000th powerful number (see the number 3 136).
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