330 Jean-Marie De Koninck

407 498 958

• possibly the largest number n such that max(P (n), P (n + 1), P (n + 2)) 100:

here

407 498 958 = 2 ·

33

· 23 · 59 · 67 · 83,

407 498 959 = 7 ·

175

· 41,

407 498 960 =

24

· 5 ·

113

· 43 · 89.

415 074 643

• the fourth prime number q which divides the sum of all the prime numbers q

(that is q|

∑

pq

p); see the number 71.

427 333 057 (= 521 · 691 · 1187)

• the smallest square-free composite number n such that p|n =⇒ p + 108|n + 108

(see the number 399).

433 494 437

• the tenth prime Fibonacci number (see the number 89).

438 579 088

• the largest number n = [d1, d2, . . . , dr] such that n =

1≤i≤r

di=0

di

di

(see the number

3 435).

455 052 511

• the number of prime numbers

1010.

459 818 240 (=

28

· 5 · 7 · 19 · 37 · 73)

• the fourth tri-perfect number (see the number 120).

472 335 975

• the second number n 1 which is equal to the sum of the ninth powers of its

digits (see the number 146 511 208).

477 638 700

• the 18th Catalan number (see the number 14).