340 Jean-Marie De Koninck

1 478 674 861

• the smallest prime number q such that

∑

p≤q

p is divisible by

p≤23

p: here

this sum is equal to 53 064 863 142 321 030 (see the number 269).

1 479 604 544

• the smallest number which can be written as the sum of four fifth powers in

three distinct ways: 1 479 604 544 =

35 +485 +525 +615

=

135 +365 +515 +645

=

185

+

365

+

445

+

665.

1 480 028 171

• the prime number p located at the center of a 3 × 3 magic square made up

entirely of prime numbers (the other eight elements of this magic square being

p ± 12, p ± 18, p ± 30 and p ± 42) and discovered by H. Nelson (R.K. Guy [101],

A6).

1 533 776 805

• the fourth number 1 which is both triangular and pentagonal:

1 533 776 805 =

55385 · 55386

2

=

31977(3 · 31977 − 1)

2

(see the number 210).

1 611 308 699

• the smallest number n such that P (n) ≤

6

√

n and P (n + 1)

6

√

n + 1: here

P (1611308699) = P

(74

· 11 ·

132

·

192)

= 19 34.23 ≈ 6

√≤

1611308699 and

P (1611308700) = P

(22

·

36

·

52

· 23 ·

312)

= 31 34.23 ≈ 6

√

1611308700 (see the

number 2

400)201.

1 622 632 573

• the 11th horse number (see the number 13).

1 631 432 881

• the seventh number which is both a triangular number and a perfect square:

1 631 432 881 =

57121(57121+1)

2

=

403912

(see the number 36).

201One can prove that this sequence is infinite: see the footnote tied to the number 2 400.