362 Jean-Marie De Koninck
252 097 800 623
the 10 000 000
000th
prime number (see the number 541).
271 818 611 107 (= 437)
the fifth number n 1 whose sum of digits is equal to
7

n (see the number
612 220 032).
275 223 438 741
the smallest number which is not a seventh power, but which can be writ-
ten as the sum of the seventh powers of some of its prime factors: here
275 223 438 741 = 3 · 23 · 43 · 92761523 =
37
+
237
+
437
(see the number 870);
at least five other numbers satisfy this property, namely 4561072096211306682,
9306119954843409393442022085025276,
343628633008268493930426179988576850614546787655,
6777869034345885139001456808449377853222864558972446987604 and
8652931112104420195217156139788964690213217995925746635175635.
285 311 670 612 (=
22
· 3 · 23 · 89 · 199 · 58367)
the 11th number of the form nn + 1 (see the number 3 126).
292 353 065 550 (= 2 ·
32
·
52
· 7 · 13 · 17 · 19 · 23 ·
312)
the smallest number which is not a prime power, but which is divisible by
the sum of the fifth powers of its prime factors, a sum which here is equal to
39352950 = 2 · 32 · 52 · 7 · 13 · 312 (see the number 378).
304 599 508 537
the smallest prime number which is followed by at least 500 consecutive compos-
ite numbers (here in fact by 513 composite numbers); see the number 370 261.
308 457 624 821
the number of 13 digit prime numbers.
311 112 122 112
the 35th insolite number (see the number 111).
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