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.
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