258 Jean-Marie De Koninck

390 625 (= 58)

• the third number n 1 whose sum of digits is equal to

4

√

n (see the number

2 401).

392 113

• the

22nd

(and the largest known) prime number pk such that p1p2 . . . pk + 1 is

prime (see the number 379).

392 448

(=28

· 3 · 7 · 73)

• the sixth Erd˝ os-Nicolas number (see the number 2 016).

393 216

• the 18th Granville number (see the number 126).

396 733

• the smallest prime number p such that p+100 is prime and such that each num-

ber between p and p + 100 is composite (see the numbers 370 261, 378 043 979,

4 758 958 741 and 22 439 962 446 379 651, as well as the table given at the number

139).

397 612

• the largest known number n = [d1, d2, . . . , dr] such that n = d1r

d

+ d2r−1

d

+ . . . +

dr1

d

: here 397 612 =

32

+

91

+

76

+

67

+

19

+

23;

the only other known number

satisfying this property is 48 625, an observation due to Patrick De Geest.

404 851

• the smallest prime number p such that p + 90 is prime and such that each

number between p and p + 90 is composite (see the number 139).

409 113

• the value of 1! + 2! + . . . + 9!.

409 619

• the eighth Hamilton number (see the number 923).