# 170,141,183,460,469,231,731,687,303,715,884,105,727/Historical Note

## Historical Note on $170 \, 141 \, 183 \, 460 \, 469 \, 231 \, 731 \, 687 \, 303 \, 715 \, 884 \, 105 \, 727$

It was Édouard Lucas who demonstrated in $1876$ that $2^{127} - 1$ is prime.

He was able to do this by using a new technique he designed, which was a precursor to the Lucas-Lehmer Test.

He himself expressed some doubt over the fact of this result, but it was confirmed in $1914$ by E. Fauquembergue.

This number held the record for the highest known prime number for longer than any other: $1876$ to $1951$, when Aimé Ferrier discovered that $\dfrac {2^{148} + 1} {17}$ is prime.

It also remains the largest prime number to be discovered without the help of modern electronic calculation machines.

The following year ($1952$) Raphael Mitchel Robinson discovered the prime nature of $2^{521} - 1$, and followed it up with $4$ others, of whch $M_{2281}$ was the largest.

To put the question into perspective, the author of this page used an online integer factorization calculator to find out the prime numbers immediately before and after $2^{127} - 1$ in a matter of seconds.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $2^{127} - 1$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $2^{2281} - 1$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $2^{127} - 1$