Apodictique arithmosophique

Valeur du premier verset : 2701

http://www.biblewheel.com/gr/GR_Database.asp?bnum=1&cnum=1&vnum=1

somme des diviseurs : s(2701 ) = 111

somme itérée : Sig (2701) = 153 = vs 17

Second verset : valeur : 3546 valeur cumulée : 6247 qui est premier

http://www.biblewheel.com/gr/GR_Database.asp?bnum=1&cnum=1&vnum=2

s(3546 ) = 4176 sig(3546) = 48923

http://arithmosophie.multiply.com/notes/item/92

la syntaxe de la commande Select est ici :

http://reference.wolfram.com/mathematica/ref/Select.html

je sélectionne sur la liste que j'ai appelé ln , les nombres premiers par :

ln = Table[ (m[[i]] + 1 + m[[i + 1]])/3 , {i, 1, 1000}]

Select [ln, PrimeQ]

qui sort :


{19, 37, 61, 79, 97, 127, 157, 193, 229, 277, 307, 337, 373, 397, \
457, 499, 523, 547, 571, 601, 619, 643, 691, 727, 757, 859, 907, 997, \
1039, 1063, 1093, 1117, 1291, 1381, 1447, 1543, 1657, 1699, 1747, \
1777, 1801, 2011, 2083, 2347, 2377, 2437, 2467, 2617, 2803, 2857, \
3001, 3037, 3217, 3307, 3319, 3361, 3697, 3877, 3907, 3931, 4111, \
4159, 4423, 4447, 4519, 4597, 4639, 4729, 4783, 4909, 4969, 4999, \
5023, 5077, 5119, 5167, 5209, 5431, 5527, 5557, 5581, 6067, 6079, \
6247, 6277, 6427, 6547, 6571, 6661, 6703, 6781, 6997, 7069, 7243, \
7411, 7699, 7993, 8017, 8233, 8293, 8353, 8377, 8419, 8467, 8527, \
8581, 8599, 8629, 8731, 8779, 8839, 9043, 9103, 9157, 9199, 9547, \
9619, 9739, 9811, 9859, 9883, 9907, 10111, 10273, 10597, 10657, \
10723, 10957, 11131, 11197, 11443, 11467, 11503, 11731, 11821, 11863, \
12157, 12277, 12433, 12517, 12697, 12763, 12907, 12973, 13003, 13297, \
13399, 13417, 13537, 13567, 13597, 13831, 13903, 14197, 14341, 14563, \
14653, 14683, 14821, 15091, 15139, 15661, 15727, 15787, 15901, 15919, \
16339, 16363, 16477, 16567, 16921, 17011, 17047, 17167, 17203, 17239, \
17257, 17401, 17443, 17497, 17659, 17713, 17851, 17911, 18127, 18211, \
18253, 18457, 18793, 18859, 18913, 19051, 19249, 19477, 19507, 20029, \
20101, 20341, 20389, 20533, 20707, 20731, 21067, 21121, 21157, 21277, \
21379, 21487, 21739, 21787, 21859, 21943, 22153, 22279, 22567, 22669, \
22699, 22777, 23203, 23557, 23623, 23917, 24007, 24061, 24109, 24547, \
24631, 24697, 24763, 25117, 25147, 25339, 25603, 25717, 25747, 25903, \
26041, 26227, 26317, 26479, 26737, 26863, 27067, 27109, 27259, 27277, \
27367, 27397, 27427, 27583, 27793, 27943, 27967, 28051, 28099, 28387, \
28411, 28447, 28513, 28657, 28813, 28843, 29059, 29077, 29179, 29587, \
29629, 29959, 30103, 30319, 30931, 31039, 31069, 31189, 31387, 31573, \
32089, 32191, 32563, 32587, 32647, 32839, 32911, 33199, 33289, 33403, \
33547, 33637, 33703, 33757, 34141, 34171, 34303, 34429, 34483, 34519, \
34549, 34591, 34693, 34843, 34939, 34981, 35527, 35677, 35731, 35863, \
36013, 36277, 36433, 36583, 36709, 36793, 36931, 37087, 37117, 37489, \
37579, 37633, 37657, 37747, 37813, 37861, 37879, 38167, 38197, 38239, \
38317, 38377, 38449, 38851, 39157, 39229, 39367, 39397, 39439, 39631, \
39733, 39841, 39877}

maintenant comment sélectionner les autres , ceux qui ne sont pas premiers ??

on les obtient par la commande :

Select[ln, ! PrimeQ[#] &]

que j'ai copiée ici :

https://oeis.org/A002808

et cela nous sort :

{115, 259, 355, 415, 667, 775, 817, 961, 1027, 1147, 1177, 1195, \
1225, 1339, 1357, 1411, 1435, 1477, 1507, 1519, 1573, 1615, 1675, \
1687, 1717, 1837, 1903, 1957, 1975, 2047, 2119, 2149, 2191, 2215, \
2263, 2323, 2359, 2407, 2455, 2479, 2527, 2581, 2599, 2665, 2737, \
2779, 2899, 2935, 2977, 3085, 3151, 3265, 3295, 3337, 3379, 3397, \
3427, 3505, 3589, 3619, 3655, 3715, 3745, 3781, 3811, 3841, 3997, \
4063, 4147, 4183, 4213, 4237, 4267, 4303, 4345, 4375, 4393, 4471, \
4555, 4669, 4699, 4819, 4849, 5137, 5155, 5287, 5335, 5371, 5467, \
5491, 5611, 5635, 5695, 5755, 5773, 5797, 5815, 5845, 5875, 5887, \
5911, 5941, 5977, 6031, 6103, 6127, 6181, 6349, 6415, 6457, 6487, \
6517, 6595, 6625, 6859, 6901, 6943, 6979, 7015, 7033, 7099, 7123, \
7147, 7189, 7267, 7327, 7453, 7483, 7513, 7585, 7657, 7765, 7807, \
7849, 7897, 7939, 7975, 8047, 8113, 8173, 8323, 8395, 8407, 8515, \
8551, 8671, 8809, 8869, 8917, 8983, 9073, 9229, 9271, 9361, 9457, \
9505, 9583, 9607, 9667, 9919, 9937, 9979, 10015, 10051, 10087, 10171, \
10231, 10255, 10345, 10417, 10435, 10447, 10471, 10507, 10537, 10561, \
10579, 10765, 10819, 10879, 10915, 10933, 11005, 11065, 11095, 11167, \
11245, 11275, 11305, 11335, 11347, 11359, 11395, 11539, 11569, 11611, \
11647, 11683, 11707, 11761, 11791, 11917, 11947, 12019, 12103, 12127, \
12139, 12181, 12199, 12229, 12259, 12295, 12325, 12355, 12571, 12631, \
12661, 12847, 12937, 12955, 13045, 13135, 13207, 13237, 13273, 13345, \
13387, 13435, 13465, 13501, 13519, 13555, 13651, 13705, 13735, 13777, \
13861, 13987, 14077, 14119, 14155, 14269, 14377, 14425, 14467, 14509, \
14539, 14605, 14635, 14725, 14761, 14917, 14977, 14995, 15025, 15175, \
15223, 15301, 15367, 15397, 15433, 15457, 15499, 15535, 15595, 15691, \
15715, 15757, 15811, 15835, 15865, 15955, 16009, 16051, 16075, 16117, \
16159, 16195, 16237, 16255, 16291, 16327, 16423, 16525, 16579, 16615, \
16675, 16723, 16753, 16777, 16801, 16819, 16849, 16975, 17071, 17125, \
17281, 17323, 17371, 17479, 17527, 17563, 17593, 17629, 17785, 17815, \
17887, 17947, 18007, 18055, 18067, 18079, 18175, 18295, 18343, 18391, \
18511, 18547, 18577, 18595, 18607, 18649, 18703, 18727, 18883, 18955, \
18997, 19021, 19075, 19093, 19123, 19147, 19189, 19279, 19315, 19399, \
19519, 19633, 19747, 19771, 19849, 19915, 19933, 19969, 20077, 20119, \
20137, 20155, 20167, 20191, 20227, 20257, 20299, 20455, 20497, 20515, \
20557, 20575, 20635, 20695, 20761, 20779, 20803, 20827, 20839, 20863, \
20893, 20917, 20989, 21097, 21427, 21553, 21631, 21685, 21829, 21877, \
21901, 21919, 21985, 22021, 22087, 22183, 22231, 22267, 22339, 22423, \
22477, 22507, 22633, 22729, 22759, 22819, 22867, 22903, 22951, 23005, \
23065, 23113, 23149, 23263, 23341, 23437, 23503, 23533, 23587, 23665, \
23701, 23749, 23803, 23845, 23881, 23965, 24037, 24175, 24217, 24259, \
24295, 24307, 24331, 24355, 24367, 24427, 24487, 24511, 24583, 24607, \
24787, 24811, 24871, 24931, 24955, 24997, 25039, 25075, 25177, 25249, \
25417, 25495, 25555, 25627, 25669, 25735, 25789, 25843, 25957, 25975, \
26005, 26059, 26077, 26125, 26185, 26269, 26377, 26443, 26509, 26593, \
26689, 26767, 26797, 26815, 26929, 26971, 27001, 27037, 27079, 27157, \
27217, 27319, 27415, 27451, 27475, 27493, 27703, 27871, 27913, 27991, \
28117, 28159, 28207, 28237, 28255, 28267, 28291, 28321, 28357, 28483, \
28543, 28567, 28609, 28699, 28765, 28897, 28981, 29041, 29095, 29107, \
29143, 29215, 29299, 29377, 29407, 29461, 29515, 29551, 29677, 29707, \
29737, 29755, 29827, 29911, 30037, 30157, 30199, 30217, 30235, 30265, \
30355, 30385, 30415, 30433, 30475, 30595, 30709, 30751, 30775, 30811, \
30847, 30877, 30973, 31009, 31129, 31279, 31435, 31471, 31507, 31519, \
31651, 31717, 31777, 31813, 31843, 31867, 31897, 31933, 31999, 32149, \
32311, 32431, 32485, 32527, 32539, 32599, 32701, 32731, 32767, 32935, \
32947, 32989, 33055, 33097, 33115, 33157, 33217, 33367, 33451, 33511, \
33571, 33727, 33793, 33847, 33919, 33985, 34063, 34117, 34237, 34333, \
34375, 34621, 34657, 34735, 34777, 34795, 34813, 34885, 35011, 35035, \
35047, 35131, 35239, 35287, 35335, 35383, 35425, 35485, 35551, 35587, \
35629, 35707, 35785, 35953, 36043, 36085, 36115, 36133, 36193, 36337, \
36367, 36379, 36403, 36463, 36517, 36631, 36661, 36763, 36817, 36859, \
36895, 37015, 37075, 37177, 37219, 37255, 37327, 37411, 37459, 37543, \
37603, 37705, 37777, 37837, 37939, 38029, 38107, 38155, 38227, 38275, \
38341, 38413, 38479, 38503, 38545, 38599, 38725, 38905, 38935, 38983, \
39037, 39091, 39187, 39307, 39421, 39463, 39487, 39553, 39661, 39697, \
39763, 39793, 39817, 39859, 39907}

http://arithmosophie.multiply.com/journal/item/40/40

on sort donc la liste par la commande :

m = Select[Range[100000], PrimeQ[#] && Mod[#, 9] == 1 &]

puis on sort simplement la table voulue par :

Table[ (m[[i]] + 1 + m[[i + 1]])/3 , {i, 1, 1000}]

qui donne :

{19, 37, 61, 79, 97, 115, 127, 157, 193, 229, 259, 277, 307, 337, \
355, 373, 397, 415, 457, 499, 523, 547, 571, 601, 619, 643, 667, 691, \
727, 757, 775, 817, 859, 907, 961, 997, 1027, 1039, 1063, 1093, 1117, \
1147, 1177, 1195, 1225, 1291, 1339, 1357, 1381, 1411, 1435, 1447, \
1477, 1507, 1519, 1543, 1573, 1615, 1657, 1675, 1687, 1699, 1717, \
1747, 1777, 1801, 1837, 1903, 1957, 1975, 2011, 2047, 2083, 2119, \
2149, 2191, 2215, 2263, 2323, 2347, 2359, 2377, 2407, 2437, 2455, \
2467, 2479, 2527, 2581, 2599, 2617, 2665, 2737, 2779, 2803, 2857, \
2899, 2935, 2977, 3001, 3037, 3085, 3151, 3217, 3265, 3295, 3307, \
3319, 3337, 3361, 3379, 3397, 3427, 3505, 3589, 3619, 3655, 3697, \
3715, 3745, 3781, 3811, 3841, 3877, 3907, 3931, 3997, 4063, 4111, \
4147, 4159, 4183, 4213, 4237, 4267, 4303, 4345, 4375, 4393, 4423, \
4447, 4471, 4519, 4555, 4597, 4639, 4669, 4699, 4729, 4783, 4819, \
4849, 4909, 4969, 4999, 5023, 5077, 5119, 5137, 5155, 5167, 5209, \
5287, 5335, 5371, 5431, 5467, 5491, 5527, 5557, 5581, 5611, 5635, \
5695, 5755, 5773, 5797, 5815, 5845, 5875, 5887, 5911, 5941, 5977, \
6031, 6067, 6079, 6103, 6127, 6181, 6247, 6277, 6349, 6415, 6427, \
6457, 6487, 6517, 6547, 6571, 6595, 6625, 6661, 6703, 6781, 6859, \
6901, 6943, 6979, 6997, 7015, 7033, 7069, 7099, 7123, 7147, 7189, \
7243, 7267, 7327, 7411, 7453, 7483, 7513, 7585, 7657, 7699, 7765, \
7807, 7849, 7897, 7939, 7975, 7993, 8017, 8047, 8113, 8173, 8233, \
8293, 8323, 8353, 8377, 8395, 8407, 8419, 8467, 8515, 8527, 8551, \
8581, 8599, 8629, 8671, 8731, 8779, 8809, 8839, 8869, 8917, 8983, \
9043, 9073, 9103, 9157, 9199, 9229, 9271, 9361, 9457, 9505, 9547, \
9583, 9607, 9619, 9667, 9739, 9811, 9859, 9883, 9907, 9919, 9937, \
9979, 10015, 10051, 10087, 10111, 10171, 10231, 10255, 10273, 10345, \
10417, 10435, 10447, 10471, 10507, 10537, 10561, 10579, 10597, 10657, \
10723, 10765, 10819, 10879, 10915, 10933, 10957, 11005, 11065, 11095, \
11131, 11167, 11197, 11245, 11275, 11305, 11335, 11347, 11359, 11395, \
11443, 11467, 11503, 11539, 11569, 11611, 11647, 11683, 11707, 11731, \
11761, 11791, 11821, 11863, 11917, 11947, 12019, 12103, 12127, 12139, \
12157, 12181, 12199, 12229, 12259, 12277, 12295, 12325, 12355, 12433, \
12517, 12571, 12631, 12661, 12697, 12763, 12847, 12907, 12937, 12955, \
12973, 13003, 13045, 13135, 13207, 13237, 13273, 13297, 13345, 13387, \
13399, 13417, 13435, 13465, 13501, 13519, 13537, 13555, 13567, 13597, \
13651, 13705, 13735, 13777, 13831, 13861, 13903, 13987, 14077, 14119, \
14155, 14197, 14269, 14341, 14377, 14425, 14467, 14509, 14539, 14563, \
14605, 14635, 14653, 14683, 14725, 14761, 14821, 14917, 14977, 14995, \
15025, 15091, 15139, 15175, 15223, 15301, 15367, 15397, 15433, 15457, \
15499, 15535, 15595, 15661, 15691, 15715, 15727, 15757, 15787, 15811, \
15835, 15865, 15901, 15919, 15955, 16009, 16051, 16075, 16117, 16159, \
16195, 16237, 16255, 16291, 16327, 16339, 16363, 16423, 16477, 16525, \
16567, 16579, 16615, 16675, 16723, 16753, 16777, 16801, 16819, 16849, \
16921, 16975, 17011, 17047, 17071, 17125, 17167, 17203, 17239, 17257, \
17281, 17323, 17371, 17401, 17443, 17479, 17497, 17527, 17563, 17593, \
17629, 17659, 17713, 17785, 17815, 17851, 17887, 17911, 17947, 18007, \
18055, 18067, 18079, 18127, 18175, 18211, 18253, 18295, 18343, 18391, \
18457, 18511, 18547, 18577, 18595, 18607, 18649, 18703, 18727, 18793, \
18859, 18883, 18913, 18955, 18997, 19021, 19051, 19075, 19093, 19123, \
19147, 19189, 19249, 19279, 19315, 19399, 19477, 19507, 19519, 19633, \
19747, 19771, 19849, 19915, 19933, 19969, 20029, 20077, 20101, 20119, \
20137, 20155, 20167, 20191, 20227, 20257, 20299, 20341, 20389, 20455, \
20497, 20515, 20533, 20557, 20575, 20635, 20695, 20707, 20731, 20761, \
20779, 20803, 20827, 20839, 20863, 20893, 20917, 20989, 21067, 21097, \
21121, 21157, 21277, 21379, 21427, 21487, 21553, 21631, 21685, 21739, \
21787, 21829, 21859, 21877, 21901, 21919, 21943, 21985, 22021, 22087, \
22153, 22183, 22231, 22267, 22279, 22339, 22423, 22477, 22507, 22567, \
22633, 22669, 22699, 22729, 22759, 22777, 22819, 22867, 22903, 22951, \
23005, 23065, 23113, 23149, 23203, 23263, 23341, 23437, 23503, 23533, \
23557, 23587, 23623, 23665, 23701, 23749, 23803, 23845, 23881, 23917, \
23965, 24007, 24037, 24061, 24109, 24175, 24217, 24259, 24295, 24307, \
24331, 24355, 24367, 24427, 24487, 24511, 24547, 24583, 24607, 24631, \
24697, 24763, 24787, 24811, 24871, 24931, 24955, 24997, 25039, 25075, \
25117, 25147, 25177, 25249, 25339, 25417, 25495, 25555, 25603, 25627, \
25669, 25717, 25735, 25747, 25789, 25843, 25903, 25957, 25975, 26005, \
26041, 26059, 26077, 26125, 26185, 26227, 26269, 26317, 26377, 26443, \
26479, 26509, 26593, 26689, 26737, 26767, 26797, 26815, 26863, 26929, \
26971, 27001, 27037, 27067, 27079, 27109, 27157, 27217, 27259, 27277, \
27319, 27367, 27397, 27415, 27427, 27451, 27475, 27493, 27583, 27703, \
27793, 27871, 27913, 27943, 27967, 27991, 28051, 28099, 28117, 28159, \
28207, 28237, 28255, 28267, 28291, 28321, 28357, 28387, 28411, 28447, \
28483, 28513, 28543, 28567, 28609, 28657, 28699, 28765, 28813, 28843, \
28897, 28981, 29041, 29059, 29077, 29095, 29107, 29143, 29179, 29215, \
29299, 29377, 29407, 29461, 29515, 29551, 29587, 29629, 29677, 29707, \
29737, 29755, 29827, 29911, 29959, 30037, 30103, 30157, 30199, 30217, \
30235, 30265, 30319, 30355, 30385, 30415, 30433, 30475, 30595, 30709, \
30751, 30775, 30811, 30847, 30877, 30931, 30973, 31009, 31039, 31069, \
31129, 31189, 31279, 31387, 31435, 31471, 31507, 31519, 31573, 31651, \
31717, 31777, 31813, 31843, 31867, 31897, 31933, 31999, 32089, 32149, \
32191, 32311, 32431, 32485, 32527, 32539, 32563, 32587, 32599, 32647, \
32701, 32731, 32767, 32839, 32911, 32935, 32947, 32989, 33055, 33097, \
33115, 33157, 33199, 33217, 33289, 33367, 33403, 33451, 33511, 33547, \
33571, 33637, 33703, 33727, 33757, 33793, 33847, 33919, 33985, 34063, \
34117, 34141, 34171, 34237, 34303, 34333, 34375, 34429, 34483, 34519, \
34549, 34591, 34621, 34657, 34693, 34735, 34777, 34795, 34813, 34843, \
34885, 34939, 34981, 35011, 35035, 35047, 35131, 35239, 35287, 35335, \
35383, 35425, 35485, 35527, 35551, 35587, 35629, 35677, 35707, 35731, \
35785, 35863, 35953, 36013, 36043, 36085, 36115, 36133, 36193, 36277, \
36337, 36367, 36379, 36403, 36433, 36463, 36517, 36583, 36631, 36661, \
36709, 36763, 36793, 36817, 36859, 36895, 36931, 37015, 37075, 37087, \
37117, 37177, 37219, 37255, 37327, 37411, 37459, 37489, 37543, 37579, \
37603, 37633, 37657, 37705, 37747, 37777, 37813, 37837, 37861, 37879, \
37939, 38029, 38107, 38155, 38167, 38197, 38227, 38239, 38275, 38317, \
38341, 38377, 38413, 38449, 38479, 38503, 38545, 38599, 38725, 38851, \
38905, 38935, 38983, 39037, 39091, 39157, 39187, 39229, 39307, 39367, \
39397, 39421, 39439, 39463, 39487, 39553, 39631, 39661, 39697, 39733, \
39763, 39793, 39817, 39841, 39859, 39877, 39907}

le nouveau problème est alors de séparer dans cette liste les nombres premiers des "exceptions", dont les premières sont :

115 = 5 x 23 , 259 = 7 x 37 , 355 = 5 x 71 , 415 = 5 x 83 , etc...

COMMENT FAIRE ???

Ils sont ici sur Sloane :

https://oeis.org/A061237

https://oeis.org/A061237/b061237.txt

(suite à laquelle on pourra ajouter 1 si on le consodière comme un nombre premier)

Ces nombres comprennent 19 , 37 , 73, soit les trois nombres "fondateurs" de l'arithmosophie de la Bible et du Coran.

Ils comprennent aussi des nombres aussi importants que 181 , 271 (le tiers de 813) , 541 = ISRAEL

Cette suite doit donc être étudiée pour elle même, et parce qu'elle pourrait bien donner un nouveau code pour la gematria.

19 x 37 = 703 = vs 37 donne en faisant la somme des diviseurs :

1 + 19 + 37 = 57 = 3 x 19

or cette propriété d'être le triple d'un nombre premeir, semble vraie pour les suivants :

1 + 37 + 73 = 111 = 3 x 37

1 + 73 + 109 = 183 = 3 x 61

1 + 109 + 127 = 237 = 3 x 79

1 + 127 + 163 = 291 = 3 x 97

1 + 163 + 181 = 345 = 3 x 5 x 23 (non vérifiée ici) = 3 x 115 (lié au nombre coranique 114 ??)

1 + 181 + 199 = 381 = 3 x 127

1 + 199 + 271 = 471 = 3 x 157

1 + 271 + 307 = 579 = 3 x 193

1 + 307 + 379 = 687 = 3 x 229

1 + 379 + 397 = 777 = 21 x 37 (non vérifié) = 3 x 259

1 + 397 + 433 = 831 = 3 x 277

1 + 433 + 487 = 921 = 3 x 307

1 + 487 + 523 = 1011 = 3 x 337

1 + 523 + 541 = 1065 = 15 x 71 (non vérifé)

http://www.bibleetnombres.online.fr/affaire_DSK_119.htm

autres pepites numeriques :

http://www.bibleetnombres.online.fr/9_11_9.htm