156 Jean-Marie De Koninck
3 465 (= 32 · 5 · 7 · 11)
the fifth odd abundant number (see the number 945).
3 507
the 19th number n such that n! 1 is prime (see the number 166).
3 511
the second (and largest known) Wieferich prime (see the number 1 093)145.
3 528
the fourth powerful number which can be written as the sum of two co-prime
3-powerful numbers = 1: 3 528 = 1 331 + 2 197, that is
23
·
32
·
72
=
113
+
133
(see the number 841).
3 570
the smallest number n 1 such that φ(n)σ(n) is a fifth power (see the numbers
51 and 170).
3 593
the fifth prime number of the form
(x4
+
y4)/2
(see the number 41): here
3 593 = (54 + 94)/2.
145It
is interesting to display the almost complete factorization of
23 510
1, a 1 057 digit number:
23 510
1 =
34
· 7 · 11 · 19 · ·31 · 73 · 79 · 131 · 151 · 271 · 331 · 631 · 811 · 937 · 1171 · 2731
·35112
· 6553 · 8191 · 10531 · 15121 · 23311 · 65521 · 86113 · 87211 · 107251
·121369 · 262657 · 348031 · 409891 · 446473 · 1024921 · 1969111 · 4633201
·7623851 · 18837001 · 22366891 · 29121769 · 409251961 · 2400314671
·7830118297 · 26959262851 · 21497866557571 · 49971617830801
·145295143558111· 385838642647891 · 571890896913727 · 93715008807883087
·194900834792501371· 339175003117573351 · 4242734772486358591
·85488365519409100951· 150832426800173710177 · 1439538040790707946401
·571403921126076957182161· 5302306226370307681801
·255375215316698521591· 4247713303224552237738169
·43725552532343303477113703251· 134304196845099262572814573351
·2728334536034592865339299805712535332071
·4897406518564079146139572699835240681611
·24841125429051585062538961751269988364169· C183 · C209,
where C183 and C209 stand for composite numbers made up respectively of 183 and 209 digits.
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