398 Jean-Marie De Koninck
23 217
1
the 18th Mersenne prime, a 969 digit number.
11 . . . 1
1 031
the fifth prime number all of whose digits are 1 (see the number 19).
2212
+ 1
the 13th Fermat number, a 1 234 digit number; it is a composite number for
which four of its prime factors are
q1 = 114689 = 7 ·
214
+ 1, q2 = 26017793 = 397 ·
216
+ 1,
q3 = 63766529 = 973 ·
216
+ 1 and q4 = 190274191361 = 11613415 ·
214
+ 1;
q1 was obtained by Pervouchine and Lucas in 1877, q2 and q3 were obtained
by Western in 1903, while q4 was discovered by Hallyburton and Brillhart in
1974, so that
2212
+ 1 = q1 · q2 · q3 · q4 · C1
202
,
where C1
202
is a composite 1 202 digit number (see the number 70 525 124 609).
24 253
1
the
19th
Mersenne prime, a 1 281 digit number.
22 202(22 203
1)
the
16th
even perfect number, a 1 327 digit number.
24 423
1
the
20th
Mersenne prime, a 1 332 digit number.
22 280(22 281
1)
the 17th even perfect number, a 1 373 digit number.
23 216(23 217 1)
the
18th
even perfect number, a 1 937 digit number.
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