Forum: Dobri
2022-05-18, 14:56
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Replies: 53
Views: 4,436
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Forum: Dobri
2022-05-14, 14:34
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Replies: 53
Views: 4,436
This update contains images of the values of the...
This update contains images of the values of the absolute minima and maxima (up to a prime x on the horizontal axis) of the prime race โ(x) = ๐6,5(x) - ๐6,1(x) for the first 185,000,000,000 primes....
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Forum: Dobri
2022-05-13, 05:43
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Replies: 26
Views: 1,637
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Forum: Lounge
2022-05-12, 14:01
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Replies: 49
Views: 2,251
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Forum: Number Theory Discussion Group
2022-05-06, 16:01
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Replies: 12
Views: 762
The Wolfram code below represents the prime...
The Wolfram code below represents the prime exponent p of each known Mersenne prime 2p-1 as a unique sum of two squares p = a2 + b2 with the exception of the prime exponents p = 4k + 3 for which...
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Forum: MattcAnderson
2022-05-02, 21:54
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Replies: 6
Views: 283
Marin Mersenne wrote about the birds that
...
Marin Mersenne wrote about the birds that
"...qu'ils se seruent de leurs voix pour exprimer leurs passions naturelles, & non des paroles..."
("...they use their voices to express their...
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Forum: Information & Answers
2022-05-02, 15:39
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Replies: 11
Views: 1,499
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Forum: Lounge
2022-04-24, 17:57
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Replies: 1,925
Views: 217,445
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Forum: Dobri
2022-04-24, 08:25
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Replies: 12
Views: 1,515
For quality assurance (QA) purposes, a stage-1...
For quality assurance (QA) purposes, a stage-1 P-1 test was performed on M726064763 without excluding in quotation marks the 12 known factors.
The result is a 145-digit 481-bit composite factor...
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Forum: No Prime Left Behind
2022-04-23, 10:42
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Replies: 24
Views: 645
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Forum: Math
2022-04-22, 11:41
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Replies: 2
Views: 850
Here is a Wolfram code to test the quoted...
Here is a Wolfram code to test the quoted heuristic recursion. :smile:
p = 1277; Mn = 2^p - 1; xn = 3;
While[(GCD[xn - 1, Mn] == 1) && (xn != 0), xn = Mod[(xn^(12*p*5) - 1)*(xn^(12*p*7) - 1) + 1,...
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Forum: Dobri
2022-04-20, 12:58
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Replies: 26
Views: 1,637
This forms a sequence of composite p values...
This forms a sequence of composite p values indeed,
p = 21, 121, 153, 221, 237, 245, 305, 333, 357, 381, 445, 465, 545, 565, 605, 637, 657, 737, 753, 777, 793, 861, 917,...
kc = 3; ic = 2;...
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Forum: Dobri
2022-04-20, 10:19
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Replies: 26
Views: 1,637
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Forum: Dobri
2022-04-20, 09:29
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Replies: 26
Views: 1,637
I just connect a Raspberry Pi 4B device to the...
I just connect a Raspberry Pi 4B device to the HDMI port of my 4K TV set and use Wolfram Mathematica for free.
Here is the Wolfram code for the Mersenne primes
MPData = {2, 3, 5, 7, 13, 17, 19,...
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Forum: Dobri
2022-04-20, 07:58
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Replies: 26
Views: 1,637
There is a typo, it has to be "... for p = 101,...
There is a typo, it has to be "... for p = 101, 137, 173, 181, 241, 257, 277, 293, 313,..."
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Forum: Dobri
2022-04-20, 06:48
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Replies: 26
Views: 1,637
Excluding p = 5 for which 25 - 1 = 6ร5 + 1 =...
Excluding p = 5 for which 25 - 1 = 6ร5 + 1 = 27ร12 + 22, there are no other counterexamples for p mod 4 = 1 and k = 3 within the limited sample of known Mersenne primes.
Starting from the...
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Forum: Dobri
2022-04-20, 05:14
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Replies: 26
Views: 1,637
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Forum: Dobri
2022-04-19, 16:25
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Replies: 26
Views: 1,637
Concerning k = 5, there are 10 known Mersenne...
Concerning k = 5, there are 10 known Mersenne primes, with prime exponents p = 3, 7, 13, 19, 31, 1279, 2203, 2281, 23209, and 44497, for which 2*5*p+1 is a prime number. Here p mod 6 = 1 for p = 7,...
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Forum: Dobri
2022-04-19, 15:52
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Replies: 26
Views: 1,637
Within the limited sample of known Mersenne...
Within the limited sample of known Mersenne primes, there are 7 Mersenne primes, with prime exponents p = 2, 5, 89, 9689, 21701, 859433, and 43112609, for which 2p + 1 is a prime number. Obviously, p...
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Forum: Dobri
2022-04-19, 15:14
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Replies: 11
Views: 1,175
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Forum: Dobri
2022-04-18, 16:17
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Replies: 11
Views: 1,175
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Forum: Dobri
2022-04-18, 14:06
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Replies: 26
Views: 1,637
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Forum: Dobri
2022-04-17, 16:08
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Replies: 26
Views: 1,637
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Forum: Dobri
2022-04-13, 19:30
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Replies: 16
Views: 1,155
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Forum: Dobri
2022-04-13, 14:22
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Replies: 16
Views: 1,155
The result was obtained for approximately one...
The result was obtained for approximately one hour while running the Wolfram code in interpreter mode on a Raspberry Pi 4B device for which Wolfram Mathematica is available for free. Compiling the...
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