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 François Édouard Anatole 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 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
- 1919: Leonard Eugene Dickson: History of the Theory of Numbers: Volume $\text { I }$ ... (previous) ... (next): Preface
- 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): $2^{127} - 1$