Those Fascinating Numbers 391
93 310 754 811 505 006 990 350 670 730
the third number which is not a fourth power, but which can be written as the
sum of the fourth powers of some of its prime factors: here
93 310 754 811 505 006 990 350 670 730
=
22
· 5 · 7 · 23 · 31 · 97 · 103 · 373 · 1193 · 8689
·2045107145539 · 2218209705651794191
=
24
+
1034
+
3734
+
11934
+
20451071455394;
the smallest number satisfying this property is 107 827 277 891 825 604 (see the
number 870).
241 573 142 393 627 673 576 957 439 049
the smallest prime factor of the number 11 . . . 1;
71
times
indeed, we have
1071 1
9
= 241573142393627673576957439049
·45994811347886846310221728895223034301839,
a factorization first obtained by Davis and Holdridge in 1984, using the quadratic
sieve due to Pomerance.
554 079 914 617 070 801 288 578 559 178 (= 2·3·11·23·31·47 059·2 259 696 349·
110 725 121 051)
the 11th (and largest known) Guiga number (see the number 30).
162 259 276 829 213 363 391 578 010 288 127
the
11th
Mersenne prime, namely
2107
1.
14 497 650 943 439 560 735 142 707 200 000 000
the fifth number which is equal to the product of the factorials of its digits in
base 12:
14 497 650 943 439 560 735 142 707 200 000 000 =
[5, 1, 0, 10, 8, 9, 9, 9, 6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]12
(see the number 21 772 800).
130 547 383 608 518 581 304 037 589 860 381 057
the smallest known number n such that

p|n
p7
divides n (see the number
378).
Previous Page Next Page