Discussion:
31 Mesenne Prime exponents n = 4k +1
(too old to reply)
Arthur Neuendorffer
2021-10-04 15:41:50 UTC
Permalink
https://en.wikipedia.org/wiki/Mersenne_prime
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31 Mesenne Prime exponents n = 4k +1
19 Mesenne Prime exponents n = 4k +3
.....................................
Chance of discrepancy ~ 1 in 9
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31 Mesenne Prime exponents n = 4k +1
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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
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19 Mesenne Prime exponents n = 4k +3
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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
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Art Neuendorffer
Arthur Neuendorffer
2021-10-08 22:43:30 UTC
Permalink
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
nordicskiv2
2021-10-09 01:38:40 UTC
Permalink
Post by Arthur Neuendorffer
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?
Post by Arthur Neuendorffer
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".]
Post by Arthur Neuendorffer
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?
Post by Arthur Neuendorffer
----------------------------
Art Neuendorffer (aka Noonedafter)
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