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Sorry I must have missed one digit while copying the result, it should be:
p=35
Ps=77777777777777777777777777777777813
p should be a prime whereas p=35=5x7, p=51=3x17, p=341=11x31
Okay that's your choice but the results Ps are prime.
BTW: there are no other results up to 16733 (including non primes).
Let d=7
p=5
Ps=77783 [only prime so far for p[n<2000]]
There are more results:
p=35
Ps=7777777777777777777777777777777781
p=51
Ps=777777777777777777777777777777777777777777777777829
p=341
Ps=77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778119
That won't solve the problem of the pseudoprimes. You can use different bases to eliminate most pseudoprimes but some are pseudo for all bases co-prime to p.
These are called Carmichael Numbers.
I'm not sure what you mean, can you give an example?
Using Fermat is very fast however this prime test is not deterministic but probabilistic. There are composite numbers that pass this test called pseudoprimes.
First results for Pt=23: (no perfect twins)
-4475 : 5889137212050938735368472902508869483835853899657458332272001992354134048771473543186122962291841184947527129
+4475 : 5889137212050938735368472902508869483835853899657458332272001992354134048771473543186122962291841184947536079
-11737- : 763535938306412512047674015563031733445522730069155715016873757788272794603779526321867531591867496118778511572255374563
+11737+ : 763535938306412512047674015563031733445522730069155715016873757788272794603779526321867531591867496118778511572255398037
-11848 : 977088126028151808796565733124095583631954744365488527199737265166828731869558855032529267557676836542668809798898003537
+11848 : 977088126028151808796565733124095583631954744365488527199737265166828731869558855032529267557676836542668809798898027233
With Windows your computer tells you what to do, with Linux your computer does what you want
Every composite number is the difference of two squares, a prime is never:
In your example
Cool very
The product of all prime numbers up to a certain prime is called a Primorial
In your post
Sometimes the algorithm also works when the result is larger than the next prime squared.
For example:
I am not sure this proves that there is an infinite number of twin primes. The algorithm often finds the same twin primes between 1 and the next largest prime squared. I think you still have to proof that a greater primorial also results in larger twin primes.
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