396 Jean-Marie De Koninck
228
+ 1
the ninth Fermat number, a 78 digit number; it is a composite number, whose
factorization was obtained in 1980 by Brent and Pollard:
228
+ 1 = 1238926361552897
·93461639715357977769163558199606896584051237541638188580280321.
398 075 086 424 064 937 397 125 500 550 386 491 199 064 362 342 526
708 406 385 189 575 946 388 957 261 768 583 317
the smallest prime factor of the RSA-576 number, a 174 digit number which
no one could factor, until December 2003; this number was finally factored by
Jens Franke, who obtained that the number
1881988129206079638386972394616504398071635633794173827007633
564229888597152346654853190606065047430453173880113033967161
99692321205734031879550656996221305168759307650257059
is the product of the two prime numbers
398075086424064937397125500550386491199064362342526708406
385189575946388957261768583317
and
472772146107435302536223071973048224632914695302097116459
852171130520711256363590397527.
229
+ 1
the tenth Fermat number, a 155 digit number: it is a composite number, and
its smallest prime factor (found by Western in 1903) is
2 424 833 = 37 ·
216
+ 1.
2521
1
the 13th Mersenne prime, a 157 digit number.
2607 1
the
14th
Mersenne prime, a 183 digit number.
2210
+ 1
the 11th Fermat number, a 309 digit number: it is a composite number, whose
smallest prime factor, namely
45 592 577 = 11 131 ·
212
+ 1,
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