256 Jean-Marie De Koninck

362 880

• the value of 9! .

364 087

• the smallest number n such that φ(n) = 9! (see the number 779).

366 439

• the

21rst

prime number pk such that p1p2 . . . pk + 1 is prime (see the number

379).

369 119

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

(that is q|

∑

pq

p); see the number 71.

369 410

• the second number which can be written as the sum of the squares of two

prime numbers in eight distinct ways (the smallest being 81 770): 369 410 =

312 + 6072 = 1032 + 5992 = 1912 + 5772 = 2292 + 5632 = 2772 + 5412 =

3132 + 5212 = 3472 + 4992 = 3892 + 4672 (see the number 338).

370 047

• the seventh composite number n such that σ(n +6) = σ(n)+6 (see the number

104).

370 261

• the smallest prime number which is followed by at least 100 consecutive com-

posite numbers (in fact, here by exactly 111 composite numbers); if qk stands

for the smallest prime number which is followed by at least 100k consecutive

composite

numbers179,

then q1 = 370 261, q2 = 20 831 323, q3 = 2 300 942 549,

q4 = 25 056 082 087, q5 = 304 599 508 537, q6 = 1 968 188 556 461 and q7 =

13 829 048 559 701 (see also the number 1 671 800).

179The

numbers qi were obtained using the table Maximal gaps between consecutive primes ≤

7.263 × 1013 in the book of H. Riesel [173], p. 80.