Those Fascinating Numbers 115
977
the fourth Stern number (see the number 137).
983
the smallest prime factor of the Mersenne number 2491 1, whose complete
factorization is given by
2491
1 = 983 · 7707719 · 110097436327057 · 6976447052525718623
·19970905118623195851890562673
·3717542676439779473786876643915388439
·14797326616665978116353515926860025681383;
it is the smallest Mersenne number with exactly seven prime factors (see the
number 223 for the list of the smallest Mersenne numbers which require a given
number of prime factors).
985
the 13th Markoff number (see the number 433).
987
the smallest number n such that ω(n)+ω(n+1)+ω(n+2)+ω(n+3) = 12: here
987 = 3·7·47, 988 = 22 ·13·19, 989 = 23·43 and 990 = 2·32 ·5·11; if we denote
by nk the smallest number n such that ω(n)+ω(n+1)+ω(n+2)+ω(n+3) = k,
we have the following table:
k nk
4 2
5 3
6 9
7 12
8 33
k nk
9 75
10 153
11 492
12 987
13 4 179
k nk
14 13 803
15 18 444
16 134 043
17 282 489
18 1 013 724
k nk
19 4 289 592
20 12 582 633
21 57 495 513
22 260 628 717
23 801 621 093
991
the ninth prime number pk such that p1p2 . . . pk 1 is prime (see the number
317);
the largest three digit number for which each permutation of its digits provides
a prime number, namely in this case the prime numbers 991, 199 and 919; the
only other known prime numbers satisfying this property are 2, 3, 5, 7, 11, 13,
17, 31, 37, 71, 73, 79, 97 as well as all the primes of the form 11 . . . 1
k
(for these
last primes, see the number 19).
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