380 Jean-Marie De Koninck
45 848 500 718 449 031 (= 719)
the second number n 1 whose sum of digits is equal to
9

n (see the number
3 904 305 912 313 344).
48 988 659 276 962 496
the smallest number n which can be written as the sum of two cubes in five
distinct ways:
48 988 659 276 962 496 =
387873
+
3657573
=
1078393
+
3627533
=
2052923
+
3429523
=
2214243
+
3365883
=
2315183
+
3319543
(D.W. Wilson [208]; see the number 1 729).
59 649 589 127 497 217
the smallest prime factor of the Fermat number F7 =
227
+ 1, whose complete
factorization is given by
F7 = 59649589127497217 · 57044689200685129054721.
60 977 817 398 996 785 (=5 · 7 · 17 · 19 · 23 · 37 · 53 · 73 · 79 · 89 · 233)
the smallest Carmichael number which is the product of 11 prime numbers (see
the number 41 041).
99 194 853 094 755 497
the 12th prime Fibonacci number (see the number 89).
99 999 999 999 999 997
the largest 17 digit prime number.
100 000 000 000 000 003
the smallest 18 digit prime number.
107 827 277 891 825 604
the smallest 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
107 827 277 891 825 604 =
22
· 3 · 7 · 31 · 67 · 18121 · 34105993
=
34
+
314
+
674
+
181214;
at least three other numbers satisfy this property, namely
48 698 490 414 981 559 698, 93 310 754 811 505 006 990 350 670 730
and 3 137 163 227 263 018 301 981 160 710 533 087 044 (see the number 870).
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