Those Fascinating Numbers 393
1 770 019 255 373 287 038 727 484 868 192 109 228 823
possibly the smallest number n such that
f(n + 1) = f(n + 2) = . . . = f(n + 8),
where f(n) stands for the product of the exponents in the factorization of n:
here the common value of f(n + i) is 6 (see the number 843).
1 831 607 359 566 125 048 834 492 989 440 000 000 000
the sixth number which is equal to the product of the factorials of its digits in
base 7:
1 831 607 359 566 125 048 834 492 989 440 000 000 000
= [2, 3, 0, 5, 5, 0, 1, 5, 1, 0, 0, 1, 4, 2, 3, 3, 3, 0, 2, 1, 6, 6, 1, 6, 2, 1, 2, 1, 2, 3, 5, 2,
4, 0, 4, 4, 5, 6, 0, 6, 2, 0, 0, 2, 2, 3, 4]7 (see the number 248 832 000).
6 153 473 687 096 578 758 448 522 809 275 077 520 433 167
the 11th Hamilton number (see the number 923).
20 988 936 657 440 586 486 151 264 256 610 222 593 863 921 (=
(2148
+ 1)/17)
the largest known prime found before the computer era (some times called the
Ferrier number), namely in 1952 by A. Ferrier (see H.C. Williams [204]).
75 445 311 584 829 283 999 739 123 702 169 600 000 000 000
the sixth number which is equal to the product of the factorials of its digits in
base 12:
75 445 311 584 829 283 999 739 123 702 169 600 000 000 000 =
[5, 1, 7, 2, 0, 7, 5, 4, 8, 6, 4, 11, 11, 4, 1, 2, 2, 8, 0, 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).
208 492 413 443 704 093 346 554 910 065 262 730 566 475 781
the fifth (and largest known) prime of the form
11
+
22
+ . . . +
nn,
here with
n = 30 (see the number 3 413).
273 457 513 497 334 816 890 950 735 729 000 448 000 000 000 000
the seventh number which is equal to the product of the factorials of its digits
in base 7:
273 457 513 497 334 816 890 950 735 729 000 448 000 000 000 000 =
[1, 2, 0, 2, 2, 0, 3, 3, 3, 4, 2, 3, 5, 5, 6, 5, 6, 2, 5, 1, 0, 1, 0, 5, 1, 1, 4, 2, 6, 5, 6, 3, 4, 4,
6, 0, 4, 2, 0, 5, 0, 1, 1, 3, 0, 2, 2, 3, 0, 4, 0, 0, 0, 3, 1, 1, 4]7
(see the number 248 832 000).
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