I am searching for primes using the set S(n,p) = p + 6n(p - n), where p stands for prime, and n non-negative integers. (Remember the postulate that was discussed around May this year; i.e. S(k,p) = p + 6k( p - n ) will produce a finite number of primes. )
Presently I am interested in p = 2^127 - 1, because it produces primes for a very good range of n. I am using primeform for my research. One of the exciting things is not always going higher and higher, but going back to some of the primes that have been produced, and seeing how much yield of primes can be obtained.
For example S(1911, 2^127 - 1 ) is a prime, i.e 6*1911*(2^127- 1 -1911) + 2^127- 1.
Next I take this prime S(1911, 12^127 - 1) and insert it in the set, and find we get a prime for n = 83, (and of course for n = 473). So things get complicated when I try to insert the last prime into to the formula. Primeform displays it as 6*83*(6*191.......912) + 2^127 - 1. Trying to paste this back into the primeform leads to the breakdown of the program, with a message saying that the program has performed something illegal. Trying to write the expression down properly and then pasting it, again I get the same error message.
Most likely I am making a mistake in writing out the expression, because it is so long, it is easy to make a mistake, such as get the position of a bracket wrong, etc.
Questions: (1) Is there a way of simplifying the algebra, so that the expression is not so long?
(2) Is it best to convert the expression into numerical form, and then how?
I really like the algebra form because I am interested in the patterns we get, but if it cannot be simplified, then I guess I have to resort to the numerical form.
Help will be highly appreciated.
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