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).