When I found in Edouard Lucas' Wikipedia page that he proved that $2^{127}-1$ is prime by hand, I wanted to see how did he do it. Unfortunately, every piece of information I find is about the Lucas-Lehmer test, that is a version of his test refined by Lehmer.

Since I wanted to do some comparisons about how many it would take to do so with a computer and a high-school multiplication algorithm (according to Wikipedia it took him $19$ years by hand) the Lucas-Lehmer test is not exactly what I am looking for. So, finally, where can I find the original test?

  • 1
    $\begingroup$ Do you have access to "Prime Numbers and Computer Methods for Factorization" by Riesel? $\endgroup$
    – Amzoti
    Sep 30, 2013 at 2:18
  • $\begingroup$ @Amzoti Uhhhm...yes... $\endgroup$
    – chubakueno
    Sep 30, 2013 at 2:41
  • $\begingroup$ @Amzoti I just found the Primality tests of Lucasian type part and it seems very interesting and promising. Thank you for pointing me to it. $\endgroup$
    – chubakueno
    Sep 30, 2013 at 2:48
  • $\begingroup$ You are very welcome, all of the original Lucas papers are available and the main one by Wagstaff (IIRC) is excellent. Regards $\endgroup$
    – Amzoti
    Sep 30, 2013 at 2:52

1 Answer 1


The relevant papers are:

  • $\begingroup$ Thank you for the references, but since I don't speak French it is a little hard to me to understand his paper. Not impossible, given the similarity with my native language, but a little painful. Is there an english version? $\endgroup$
    – chubakueno
    Sep 30, 2013 at 2:45
  • $\begingroup$ Not that I know of. $\endgroup$ Sep 30, 2013 at 2:49

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