Those Fascinating Numbers 177
7 912
the sixth bizarre number (see the number 70).
7 919
the 1
000th
prime number (see the number 541).
7 936
the ninth Euler number (see the number 272).
8 042
the largest known number which cannot be written as a sum of less than seven
cubes (of non negative integers): here 8 042 =
53
+
63
+
63
+
83
+
93
+
113
+
173
(see E.W. Weisstein [201], p. 1918).
8 064 (= 27 · 32 · 7)
the fifth number n having at least two distinct prime factors and such that
B1(n) = β(n)2: here 27 + 32 + 7 = (2 + 3 + 7)2 (see the number 144).
8 128
the fourth perfect number (see the number 6);
the
13th
Granville number (see the number 126).
8 169
the number of twin prime pairs 106 (see the number 1 224).
8 190
the seventh number which is not perfect or multi-perfect but whose harmonic
mean is an integer (see the number 140);
the third Erd˝ os-Nicolas number (see the number 2 016).
8 191
the fifth Mersenne prime: 8 191 =
213
1;
the smallest counter example Mq =
2q
−1 to the statement “If Mq is a Mersenne
prime, then MMq is prime”; indeed, M8
191
is composite since it is divisible by
338 193 759 479;
the largest known prime number p such that P
(p2
−1) 13 and P
(p2
−1) = 13
(see the number 4 801).
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