137,438,953,471

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Number

$137 \, 438 \, 953 \, 471$ is:

$223 \times 616 \, 318 \, 177$

The $4$th Mersenne number after $2047$, $8 \, 388 \, 607$, $536 \, 870 \, 911$ which is composite:

$137 \, 438 \, 953 \, 471 = 2^{37} - 1 = 223 \times 616 \, 318 \, 177$

The $12$th Mersenne number after $3$, $7$, $31$, $127$, $2047$, $8191$, $131 \, 071$, $524 \, 287$, $8 \, 388 \, 607$, $536 \, 870 \, 911$, $2 \, 147 \, 483 \, 647$:

$137 \, 438 \, 953 \, 471 = 2^{37} - 1$

Historical Note

$137 \, 438 \, 953 \, 471$ was the $3$rd Mersenne number to be demonstrated composite.

This was done in $1640$ by Pierre de Fermat, who demonstrated it had $223$ as a divisor.

It is in fact the $4$th Mersenne number in sequence to be composite.

However, the status of the $3$rd such composite Mersenne number, $536 \, 870 \, 911$, was not established until Leonhard Paul Euler's work in $1732$.

Also see

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