Composite Mersenne Number/Examples/M227

Example of Composite Mersenne Number

$M_{227}$ (that is, $2^{227} - 1$) is a composite number:

\(\ds 2^{227} - 1\) \(=\) \(\ds 215 \, 679 \, 573 \, 337 \, 205 \, 118 \, 357 \, 336 \, 120 \, 696 \, 157 \, 045 \, 389 \, 097 \, 155 \, 380 \, 324 \, 579 \, 848 \, 828 \, 881 \, 993 \, 727\)
\(\ds \) \(=\) \(\ds 26 \, 986 \, 333 \, 437 \, 777 \, 017 \times 7 \, 992 \, 177 \, 738 \, 205 \, 979 \, 626 \, 491 \, 506 \, 950 \, 867 \, 720 \, 953 \, 545 \, 660 \, 121 \, 688 \, 631\)
\(\ds \) \(=\) \(\ds \left({2 \times 59 \, 441 \, 263 \, 078 \, 804 \times 227 + 1}\right) \times \left({2 \times 17 \, 603 \, 915 \, 722 \, 920 \, 659 \, 970 \, 245 \, 610 \, 023 \, 937 \, 711 \, 351 \, 422 \, 158 \, 858 \, 345 \times 227 + 1}\right)\)


Historical Note

was one of a set of $6$ demonstrated to be composite by Horace Scudder Uhler using a manual desk calculator in the $1940$s.

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