Those Fascinating Numbers 343
2 214 408 306 (= 2 · 3 · 11 · 23 · 31 · 47 057)
the fifth Giuga number: the smallest four are 30, 858, 1722 and 66 198.
2 300 942 549
the smallest prime number which is followed by at least 300 consecutive compos-
ite numbers (in fact here by exactly 319 composite numbers); see the number
370 261.
2 372 890 624
the smallest number which is the first of three consecutive numbers each being
divisible by a seventh power: here 2 372 890 624 =
212
·13·44563, 2 372 890 625 =
57
· 7 · 4339 and 2 372 890 626 = 2 ·
38
· 67 · 2699 (see the number 1 375).
2 463 803 977
the second number n such that βI (n) = βI (n + 1) = βI (n + 2), where βI (n) :=

p|n,p2
p: here
2 463 803 977 = 97 · 4817 · 5273
2 463 803 978 = 2 · 233 · 563 · 9391
2 463 803 979 = 3 · 7 · 13 · 983 · 9181,
so that the common value of βI (n + i) is 10 187 (see the number 5 694).
2 468 053 248
the
24th
number n such that φ(n) + σ(n) = 3n (see the number 312).
2 550 183 799
the smallest prime factor of the Mersenne number 2103 1, whose complete
factorization is given by
2103
1 = 2 550 183 799 · 3 976 656 429 941 438 590 393.
2 971 215 073
the
16th
prime Fibonacci number (see the number 89).
3 195 380 868
the smallest number n such that Ω(n) = Ω(n + 1) = . . . = Ω(n + 11): here the
common value is 4 (see the number 602).
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