Original Lucas sequences primality test

Question

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?

Do you have access to "Prime Numbers and Computer Methods for Factorization" by Riesel? — Amzoti, Sep 30 '13 at 02:18
@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. — chubakueno, Sep 30 '13 at 02:48
You are very welcome, all of the original Lucas papers are available and the main one by Wagstaff (IIRC) is excellent. Regards — Amzoti, Sep 30 '13 at 02:52

score 3 · Accepted Answer · answered Sep 30 '13 at 02:22

3

The relevant papers are:

"Théorie des Fonctions Numériques Simplement Périodiques [I]," American Journal of Mathematics , Vol. 1, No. 2 (1878), pp. 184-196. http://www.jstor.org/stable/2369308
"Théorie des Fonctions Numériques Simplement Périodiques [II]," American Journal of Mathematics , Vol. 1, No. 4 (1878), pp. 289-321. http://www.jstor.org/stable/2369373

answered Sep 30 '13 at 02:22

Daniel McLaury

24,656

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? – chubakueno Sep 30 '13 at 02:45
Not that I know of. – Daniel McLaury Sep 30 '13 at 02:49

Original Lucas sequences primality test

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