What Mersenne primes 2^p - 1 are known, and when, how and by whom was each one found?

additional Mersenne primes:
  2^21701 - 1
  2^23209 - 1
  2^44497 - 1    [1979]
  2^86243 - 1    [1983]
  2^132049 - 1   [1983]
  2^216091 - 1   [1985]

-- Gerald A. Edgar <gae@osupyr.UUCP>

In article <11192@shemp.UCLA.EDU> Eric Behr writes:
> Since large primes have no relevance whatsoever to my favorite hobbies,
> I did not listen carefully - but I'm *sure* an NPR report about a week
> ago mentioned another record-setting Mersenne; either the journalist was
> wrong or we're all behind the times... ???

My co-worker Roger Frye found an article about this most recent
discovery in _Science_News_ for February 6, 1988.  The Mersenne prime
discovered by Walter N. Colquitt is 2^110,503 - 1.  It's not a record,
but it was overlooked in previous searches.  The article explains that
some record-setting searches weren't exhaustive.  There may be other
undiscovered Mersenne primes less than the largest known (currently
2^216,091 - 1).

Thanks to the unswerving dedication of sci.math readers, I'm now aware
of the following Mersenne primes and discovery dates.  According to
the Science News article thirty-one are known, so this must be the
complete list to date:

1. 2^2 - 1 [1644]       12. 2^127 - 1 [1644]    23. 2^11213 - 1
2. 2^3 - 1 [1644]       13. 2^521 - 1           24. 2^19937 - 1
3. 2^5 - 1 [1644]       14. 2^607 - 1           25. 2^21701 - 1
4. 2^7 - 1 [1644]       15. 2^1279 - 1          26. 2^23209 - 1
5. 2^13 - 1 [1644]      16. 2^2203 - 1          27. 2^44497 - 1    [1979]
6. 2^17 - 1 [1644]      17. 2^2281 - 1          28. 2^86243 - 1    [1983]
7. 2^19 - 1 [1644]      18. 2^3217 - 1          29. 2^110503 - 1   [1987]
8. 2^31 - 1 [1644]      19. 2^4253 - 1          30. 2^132049 - 1   [1983]
9. 2^61 - 1 [1886]      20. 2^4423 - 1          31. 2^216091 - 1   [1985]
10. 2^89 - 1 [1911]     21. 2^9689 - 1
11. 2^107 - 1 [1914]    22. 2^9941 - 1

(The date for the 29th entry is assumed.  Since it's in the February
8th issue of Science News, I suppose it was found sometime last year.)

-- Ephraim Vishniac <ephraim@think.com>

During my Mersenne prime search, I did a historical search of the
history of such primes.  Below is an updated version of that list:

[ Editor: the table below is the corrected version that Noll posted a
little later ("Here is the list again, with a few corrections"); the
first version gave Euler's date as 1722 and Lucas's as 1876, and lacked
the 1886 entries for 61.  "Nocomachus" and "Fauquemberue" in the
original are corrected to Nicomachus and Fauquembergue throughout. ]

[date is in year, month-year or day-month-year format]
[? indicates I am looking for a more exact date]
[multiple dates represent an incomplete list of early references]
[p is listed in order that 2^p-1 was shown to be prime]
[4423 was proven prime by the IBM after 4253, but
 Hurwitz & Selfridge read the results in reverse order]

p       machine         date            who
--------------------------------------------------------------
2                       500BC?          Pythagoras
                        465BC?          Eudoxus
                        275BC?          Euclid
                        100AD?          Nicomachus
3                       500BC?          Pythagoras
                        465BC?          Eudoxus
                        275BC?          Euclid
                        100AD?          Nicomachus
5                       275BC?          Euclid
                        100AD?          Nicomachus
7                       275BC?          Euclid
                        100AD?          Nicomachus
13                      1456            Monac
17                      1588            Cataldi
19                      1588            Cataldi
31                      1772            Euler
127     calculator      1875            Lucas
61      calculator      1883            Pervouchine
        calculator      1886            Pervushin
        calculator      1886            Seelhoff
        calculator      1917            Fauquembergue
89      calculator      6-1911?         Powers
        calculator      1917?           Fauquembergue
107     calculator      6-1914?         Powers
        calculator      1917?           Fauquembergue
521     SWAC            30-1-1952       Robinson, Lehmer
607     SWAC            30-1-1952       Robinson, Lehmer
1279    SWAC            26-6-1952       Robinson, Lehmer
2203    SWAC            7-10-1952       Robinson, Lehmer
2281    SWAC            9-10-1952       Robinson, Lehmer
3217    BESK            8-9-1957        Riesel
4423    IBM7090         3-11-1961       Hurwitz, Selfridge
4253    IBM7090         3-11-1961       Hurwitz, Selfridge
9689    Illiac II       11-5-1963       Gillies
9941    Illiac II       16-5-1963       Gillies
11213   Illiac II       2-6-1963        Gillies
19937   IBM360/91       4-3-1978        Tuckerman
21701   Cyber 174       30-10-1978      Noll (that me), Nickel
23209   Cyber 174       9-2-1979        Noll (same me :-})
44497   Cray 1          8-4-1979        Nelson, Slowinski
86243   Cray 1          25-9-1982       Slowinski
132049  Cray 1-XMP      1983?           Slowinski
216091  Cray 2          29-9-1984?      Slowinski
110503 [Editor: "110513" in the original]
        NEC SX-2        2-2-1988?       Colquitt, Welsh

Does anyone have a better date for the 132049 discovery?  (or any of
the other '?' dates for that matter)

While I am asking questions:  When was the last time that a
non-Mersenne prime was the largest known prime?  What was that number
and who discovered it?  My guess is that Mersenne primes have been the
largest known since at least Cataldi's discovery in 1588.  But I don't
know what record he displaced.

-- chongo [ Editor: Noll, of the table entries for 21701 and 23209 ]

[ Editor: the exponent of Colquitt and Welsh's prime is 110503, as in
the Science News report quoted above. ]

[ Editor: see also arithmetic/largest.non.mersenne.prime. ]