Those Fascinating Numbers 175
7 314
the smallest number n such that ω(n) = ω(n + 1) = 4: here 7 314 = 2 · 3 · 23 · 53
and 7 315 = 5 · 7 · 11 · 19 (see the number 230).
7 321
the seventh prime number of the form
(x4
+
y4)/2
(see the number 41): here
7 321 =
(14
+
114)/2.
7 385
the 15th Keith number (see the number 197).
7 425
the fourth of the existing eight primitive non deficient numbers (see the number
945).
7 436
the fourth number which does not produce a palindrome by the 196-algorithm
(see the number 196).
7 487
the smallest prime factor of the Mersenne number
2197
1, whose complete
factorization is given by
2197
1 = 7487
·26828803997912886929710867041891989490486893845712448833.
7 517
the 1
000th
prime power, namely here a prime number (see the number 419).
7 549
the largest known prime number p such that p−k2 is composite for each number
k

p; the other known prime numbers satisfying this property are 2, 5, 13,
31, 37, 61, 127, 379, 439, 571, 829, 991, 1 549 and 3 319 (see also the number
367).
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