Those Fascinating Numbers 389
357 686 312 646 216 567 629 137
the largest known left truncatable prime number (see the number 73 939 133).
514 843 556 263 457 213 182 265
the integer part of
ee4
, that is the expected size of the fourth prime factor of
an integer (see the number 1 618).
1 337 735 048 956 150 266 042 387
possibly the third number n for which P (n)4|n and P (n + 1)4|(n + 1): here
1 337 735 048 956 150 266 042 387 = 3 · 13 · 109 · 157 · 359 · 619 ·
17334,
1 337 735 048 956 150 266 042 388 =
22
· 37 · 53 · 97 · 193 · 557 ·
20114;
see the number 11 859 210.
2 264 832 171 464 196 096 000 000
the smallest number 2 which is equal to the product of the factorials of its
digits in base 9:
2 264 832 171 464 196 096 000 000
= [3, 1, 3, 4, 7, 6, 3, 6, 2, 1, 0, 4, 2, 1, 5, 5, 7, 4, 0, 0, 0, 0, 0, 0, 0, 0]9;
the only other number satisfying this property is
5710173055517882232971824426980147122993891075309515277598720000000000000000000
(see the number 17 280 for the list of the smallest numbers with this property
in a given base).
2 512 088 574 784 743 818 066 896
possibly the fourth number n for which P (n)4|n and P (n + 1)4|n + 1: here
2 512 088 574 784 743 818 066 896 =
24
· 7 ·
115
· 17 ·
192
·
1072
·
2114,
2 512 088 574 784 743 818 066 897 = 193 · 197 · 269 · 389 · 397 ·
11234;
see the number 11 859 210.
8 230 545 258 248 091 551 205 888
the smallest known number (found by D.W. Wilson [208]) which can be written
as the sum of two cubes in six distinct ways:
8 230 545 258 248 091 551 205 888 = 11 239
3173
+ 201 891
4353
= 17 781
2643
+ 201 857
0643
= 63 273
1923
+ 199 810
0803
= 85 970
9163
+ 196 567
5483
=
1254363283
+
1842692963
=
1593634503
+
1611279423
(see the number 1 729).
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