20210124, 11:47  #1 
Aug 2020
2^{4} Posts 
The "Hugo"est Prime Number in the world
The Largest Prime Number in the world
We can find bigger prime numbers with this method instead of using Mersenne method. https://www.researchgate.net/publica...r_in_the_world 
20210124, 13:05  #2 
Jun 2003
4914_{10} Posts 
You say that 2/(29+13*sqrt(5)) = 1/29. Basically an irrational number = a rational number. That is nonsense.
You haven't mentioned how you obtain your "Hugo" number for a given prime index. For example, how did you get Hugo(31) = 169746333457? Please explain the algorithm. You haven't mentioned how you test/prove a "Hugo" number prime. Please explain the algorithm and its runtime complexity. Finally, you're comparing the n'th "Hugo" prime to n'th Mersenne prime. That is meaningless. In fact, it merely shows that "Hugo" primes are rarer than Mersenne primes. That's actually a bad thing. A class of numbers is suitable for prime finding if there is a fast algorithm for proving them and they have higher than average probability (compared to normal numbers of same size) of being prime. You have not discussed either of these aspects. Last fiddled with by axn on 20210124 at 13:05 
20210124, 13:11  #3  
"Viliam Furík"
Jul 2018
Martin, Slovakia
2×223 Posts 
Quote:


20210206, 23:15  #4 
Aug 2020
10_{16} Posts 
Generating Large Prime Numbers
Generating Large Prime Numbers
We can find bigger prime numbers with this method. https://www.researchgate.net/publica..._Prime_Numbers 
20210207, 00:28  #5 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
29·211 Posts 
Please go ahead and find a "bigger prime number" than M82589933.
We'll wait. 
20210207, 06:21  #6  
"Kebbaj Reda"
May 2018
Casablanca, Morocco
2×41 Posts 
Quote:
M82589934!: Last fiddled with by Kebbaj on 20210207 at 06:31 

20210207, 08:04  #7  
"Kebbaj Reda"
May 2018
Casablanca, Morocco
2×41 Posts 
Quote:
but we can better calculate 2 ^p1 and test it? Last fiddled with by Kebbaj on 20210207 at 08:08 

20210207, 11:01  #8  
"Kebbaj Reda"
May 2018
Casablanca, Morocco
52_{16} Posts 
Quote:
2161 is the next term of your interesting sequance: {2, 3, 5, 7, 13, 19, 31, 43, 61, 67, 107, 127, 521, 631, 1307, 1619, 2161} The problem is the proof! / For exemple the term : 2161 which gives a prime number p = 669520952365187012801734773019730340904793566535457142176946739102321502083823099233857142333677031001451069065917971920110393630255782323617275383 212943748551754288384925199630904669367417248891744299566974703517081390275022885309341549249834446417882777235101767661916361693393317355973961109 361740840788086806308743519390960721768560920934486478379127638410123621994632671617516986749436025270882460170612028677207126354071432082804057852 021567294421457263622220997051953206302416515543266086449620395149849240412230511874765922927106048987389425173585248222630010387862113520387585603 833357934162639402504305302892121580407987900770723163143549061197642212314715010925653640972117561263171417335716694379646482116883767036278222571 382751325272483972072844735317113952796000534401 K.caldwel will not accept it, if you do not know how to factoring p1 or p + 1 in the helper. factoring p1 is difficult for this small number: 2 * 7 * 3 * 1 * 5 * 2 * 7 * 1 * 11 * 1 * 13 * 1 * 17 * 1 * 19 * 1 * 31 * 1 * 61 * 1 * 163 * 1 * 181 * 1 * 433 * 1 * 2161 ** 8641 * 1 * 151201 * 84313972619 * 1163620706029 * ... we do not talking if it is a large number. Last fiddled with by Kebbaj on 20210207 at 11:10 

20210207, 11:02  #9  
"Kebbaj Reda"
May 2018
Casablanca, Morocco
2×41 Posts 
Quote:
If you want the mathematica code for publication : d = {}; For[i = 1, i <= 326, i++, a = Prime[i]; sol = Solve[x^(2/a)  3 x^(4/a) + 1 == 0, x]; p = ToExpression[ StringCases[ToString[Numerator[RootReduce[(x /. sol[[1]])^2]]], WordCharacter ..][[1]]]; If[PrimeQ[p], AppendTo[d, a]]]; d Last fiddled with by Kebbaj on 20210207 at 11:26 

20210207, 11:45  #10 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
5029_{10} Posts 
82 589934 = 2 × 3 × 7 × 1 966427
so M82589934 or M(82589934!) mod 3 = 0. Not a long wait. https://www.mersenneforum.org/showpo...13&postcount=4 
20210207, 14:36  #11  
"Kebbaj Reda"
May 2018
Casablanca, Morocco
2·41 Posts 
Quote:
thank you! On the other hand, could you tell if 25463 is the next one on Hugo's sequance? 2,3,5,7,13,19,31,43,61,67,107,127,521,631,1307,1619,2161,..... Last fiddled with by Kebbaj on 20210207 at 14:38 

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