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  • 31 Mesenne Prime exponents n = 4k +1

    From Arthur Neuendorffer@21:1/5 to All on Mon Oct 4 08:41:50 2021
    https://en.wikipedia.org/wiki/Mersenne_prime ---------------------------------------------
    31 Mesenne Prime exponents n = 4k +1
    19 Mesenne Prime exponents n = 4k +3
    .....................................
    Chance of discrepancy ~ 1 in 9
    ------------------------------------------
    31 Mesenne Prime exponents n = 4k +1
    ---------------------------------------
    1 5 = 1^2 + 2^2
    2 13 = 2^2 + 3^2
    3 17 = 1^2 + 4^2
    4 61 = 5^2 + 6^2
    5 89 = 5^2 + 8^2
    6 521 = 11^2 + 20^2
    7 2281 = 16^2 + 45^2
    8 3217 = 9^2 + 56^2
    9 4253 = 38^2 + 53^2
    10 9689 = 35^2 + 92^2
    11 9941 = 70^2 + 71^2
    12 11213 = 67^2 + 82^2
    13 19937 = 76^2 + 119^2
    14 21701 = 26^2 + 145^2
    15 23209 = 40^2 + 147^2
    16 44497 = 64^2 + 201^2
    17 132049 = 120^2 + 343^2
    18 859433 = 187^2 + 908^2
    19 1398269 = 610^2 + 1,013^2
    20 2976221 = 1,189^2 + 1,250^2
    21 3021377 = 244^2 + 1,721^2
    22 6972593 = 352^2 + 2,617^2
    23 13466917 = 2,241^2 + 2,906^2
    24 30402457 = 3,291^2 + 4,424^2
    25 32582657 = 3,536^2 + 4,481^2
    26 42643801 = 285^2 + 6,524^2
    27 43112609 = 3,880^2 + 5,297^2 ..............................................
    28? 57885161 = 2,444^2 + 7,205^2
    29? 74207281 = 2,716^2 + 8,175^2
    30? 77232917 = 2,329^2 + 8,474^2
    31? 82589933 = 5,122^2 + 7,507^2 ---------------------------------------------
    19 Mesenne Prime exponents n = 4k +3
    ---------------------------------------
    0 2
    ......................
    1 3
    2 7
    3 19
    4 31
    5 107
    6 127
    7 607
    8 1279
    9 2203
    10 4423
    11 86243
    12 110503
    13 216091
    14 756839
    15 1257787
    16 20996011
    17 24036583
    18 25964951
    19 37156667
    ----------------------------
    Art Neuendorffer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Arthur Neuendorffer@21:1/5 to All on Fri Oct 8 15:43:30 2021
    https://en.wikipedia.org/wiki/Mersenne_prime ---------------------------------------------
    31 Mesenne Prime exponents n = 4k +1
    19 Mesenne Prime exponents n = 4k +3
    .....................................
    Chance of discrepancy ~ 1 in 9
    ---------------------------------------
    31 Mesenne Prime exponents n = 4k +1
    ---------------------------------------
    1 5 = 1^2 + 2^2
    2 13 = 2^2 + 3^2
    3 17 = 1^2 + 4^2
    4 61 = 5^2 + 6^2
    5 89 = 5^2 + 8^2
    6 521 = 11^2 + 20^2
    7 2281 = 16^2 + 45^2
    8 3217 = 9^2 + 56^2
    9 4253 = 38^2 + 53^2
    10 9689 = 35^2 + 92^2
    11 9941 = 70^2 + 71^2
    12 11213 = 67^2 + 82^2
    13 19937 = 76^2 + 119^2
    14 21701 = 26^2 + 145^2
    15 23209 = 40^2 + 147^2
    16 44497 = 64^2 + 201^2
    17 132049 = 120^2 + 343^2
    18 859433 = 187^2 + 908^2
    19 1398269 = 610^2 + 1,013^2
    20 2976221 = 1,189^2 + 1,250^2
    21 3021377 = 244^2 + 1,721^2
    22 6972593 = 352^2 + 2,617^2
    23 13466917 = 2,241^2 + 2,906^2
    24 30402457 = 3,291^2 + 4,424^2
    25 32582657 = 3,536^2 + 4,481^2
    26 42643801 = 285^2 + 6,524^2
    27 43112609 = 3,880^2 + 5,297^2
    ...................................
    28? 57885161 = 2,444^2 + 7,205^2
    29? 74207281 = 2,716^2 + 8,175^2
    30? 77232917 = 2,329^2 + 8,474^2
    31? 82589933 = 5,122^2 + 7,507^2
    --------------------------------------
    19 Mesenne Prime exponents n = 4k +3
    --------------------------------------
    0 2
    ......................
    1 3 : 7
    2 7 : 3 x 5
    3 19 : 3 x 13
    4 31 : 3 x 3 x 7
    5 107 : 5 x 43
    6 127 : 3 x 5 x 17
    7 607 : 3 x 3 x 3 x 3 x 3 x 5
    8 1279 : 3 x 853
    9 2203 : 3 x 13 x 113
    10 4423 : 3 x 3 x 983
    11 86243 : 7 x 41 x 601
    12 110503 : 3 x 23 x 3203
    13 216091 : 3 x 144061
    14 756839 : 41 x 36919
    15 1257787 : 3 x 5 x 5 x 17 x 1973
    16 20996011 : 3 x 17 x 823373
    17 24036583 : 3 x 3 x 5341463
    18 25964951 : 41 x 1266583
    19 37156667 : 5 x 2693 x 5519
    ----------------------------------------
    Art Neuendorffer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From nordicskiv2@21:1/5 to aka Noonedafter on Fri Oct 8 18:38:40 2021
    On Monday, October 4, 2021 at 11:41:52 AM UTC-4, [email protected] (aka Noonedafter) wrote:

    https://en.wikipedia.org/wiki/Mersenne_prime ---------------------------------------------
    31 Mesenne [sic] Prime exponents n = 4k +1
    19 Mesenne [sic] Prime exponents n = 4k +3 .....................................
    Chance of discrepancy ~ 1 in 9

    Huh? What is this supposed to mean, Art?

    31 Mesenne [sic]

    Who do you think (usual disclaimer) "Mesenne" is, Art? Do you realize that the flag of Mesen, Belgium displays an emblem of the Priory of Sion, Art?! [Hint: Do a Google image search for "Mesenne".]

    Prime exponents n = 4k +1
    ---------------------------------------
    1 5 = 1^2 + 2^2
    2 13 = 2^2 + 3^2
    3 17 = 1^2 + 4^2
    4 61 = 5^2 + 6^2
    5 89 = 5^2 + 8^2
    6 521 = 11^2 + 20^2
    7 2281 = 16^2 + 45^2
    8 3217 = 9^2 + 56^2
    9 4253 = 38^2 + 53^2
    10 9689 = 35^2 + 92^2
    11 9941 = 70^2 + 71^2
    12 11213 = 67^2 + 82^2
    13 19937 = 76^2 + 119^2
    14 21701 = 26^2 + 145^2
    15 23209 = 40^2 + 147^2
    16 44497 = 64^2 + 201^2
    17 132049 = 120^2 + 343^2
    18 859433 = 187^2 + 908^2
    19 1398269 = 610^2 + 1,013^2
    20 2976221 = 1,189^2 + 1,250^2
    21 3021377 = 244^2 + 1,721^2
    22 6972593 = 352^2 + 2,617^2
    23 13466917 = 2,241^2 + 2,906^2
    24 30402457 = 3,291^2 + 4,424^2
    25 32582657 = 3,536^2 + 4,481^2
    26 42643801 = 285^2 + 6,524^2
    27 43112609 = 3,880^2 + 5,297^2 ..............................................
    28? 57885161 = 2,444^2 + 7,205^2
    29? 74207281 = 2,716^2 + 8,175^2
    30? 77232917 = 2,329^2 + 8,474^2
    31? 82589933 = 5,122^2 + 7,507^2 ---------------------------------------------
    19 Mesenne [sic] Prime exponents n = 4k +3 ---------------------------------------
    0 2
    ......................
    1 3
    2 7
    3 19
    4 31
    5 107
    6 127
    7 607
    8 1279
    9 2203
    10 4423
    11 86243
    12 110503
    13 216091
    14 756839
    15 1257787
    16 20996011
    17 24036583
    18 25964951
    19 37156667

    Was there supposed to be any point whateVER to the above effusion of nutcase numerology, Art? If so, what was it?

    More to the point, was the above effusion of lunatic logorrhea supposed to have anything whateVER to do with Shakespeare, Art? You do realize that this is a Shakespeare newsgroup, don't you, Art?

    ----------------------------
    Art Neuendorffer (aka Noonedafter)

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)