Those Fascinating Numbers 319

91 963 648 (= 28 · 7 · 19 · 37 · 73)

• the second solution of

σ(n)

n

=

5

2

: the smallest solution is 24.

93 625 991

• the first member p of the fourth 8-tuple (p, p + 2, p + 6, p + 8, p + 12, p + 18, p +

20, p + 26) made up entirely of prime numbers: the smallest 8-tuple satisfying

this property is (11, 13, 17, 19, 23, 29, 31, 37), while the second and third are

those beginning respectively with 15 760 091 and 25 658 441.

95 949 311

• the first term of the smallest sequence of 16 consecutive consecutive prime

numbers all of the form 4n + 3 (see the number 463).

98 690 561

• the smallest prime number p such that Ω(p − 1) = Ω(p + 1) = 12: here

98 690 650 = 29 · 5 · 19 · 2029 and 98 690 562 = 2 · 39 · 23 · 109 (see the number

271).

98 754 210

• the only eight digit self replicating number (see the number 954).

98 765 431

• the largest prime number made up of eight distinct digits (see the number

9 871).

99 523 456

• the

16th

dihedral perfect number (see the number 130).

99 999 989

• the largest eight digit prime number.

100 000 007

• the smallest nine digit prime number.