262 Jean-Marie De Koninck
481 899
the
12th
and largest known number n 1 such that n ·
2n
+ 1 is prime (see the
number 141).
485 475
the smallest number n such that (n +
j)4
+ (n + j +
1)4,
for j = 0, 1, 2, 3, 4, are
all primes: here these primes are 111096215892626372264401,
111097131255474983589617, 111098046623980093284097,
111098961998141724650737 and 111099877377959900992481.
491 531
the largest prime number p
232
such that
7p−1
1 (mod
p2):
the only
other known prime number p satisfying this property is p = 5.
505 925
the largest known solution of γ(n + 1) γ(n) = 17 (see the number 1 681).
507 904
the
19th
Granville number (see the number 126).
509 203
the largest known Riesel number: an odd number k is called a Riesel number
if k · 2n 1 is composite for each number n 1: H. Riesel [172] proved that
k = 509 203 satisfies this property182 (see also the number 78 557).
512 000
the smallest number n such that 10! divides 1 + 2 + . . . + n (see the number
224).
514 229
the ninth prime Fibonacci number (see the number 89).
522 752
the seventh solution of σ(n) = 2n + 2 (see the number 464).
182Riesel also proved that there exist infinitely many Riesel numbers: he did this by showing that
the numbers 509203 + 11184810r, r = 0, 1, 2, . . ., are all Riesel numbers. As of May 2009, we know
that the smallest number k which could possibly be a Riesel number is k = 2 293.
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