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ramsey2879
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Ramsey Primes are those generated from a simple criteria that is easy to check. I checked all odd numbers from 1 to 1 million and 29455 numbers met the criteria. None were composite.
The check is to do the following sequence mod P and check to see that the (P-1)/2 term is zero and no term prior to that is zero.
The test sequence is S(0) = 2, S(1) = 3, S(n) = 6*S(n-1) - S(n-2) - 6. If P is prime, then S((P-1)/2) is divisible by P, but I am interested in a test that is valid only for primes. S((35-1)/2) is divisible by 35 but that is not the first term divisible by 35. Only primes seem to meet the more restricted criteria, i.e. have no term divisible by P prior to S((P-1)/2).
The first two Ramsey primes are 11 and 13 which I call a Ramsey Twin. The largest Ramsey Twin under 1 million is (998651, 998653).
Any thoughts are welcome.
Edit So far about 5 in 13 primes are Ramsey Primes so my test has limited value unless it can be proven that only primes can meet the test. Any way to prove this?
The check is to do the following sequence mod P and check to see that the (P-1)/2 term is zero and no term prior to that is zero.
The test sequence is S(0) = 2, S(1) = 3, S(n) = 6*S(n-1) - S(n-2) - 6. If P is prime, then S((P-1)/2) is divisible by P, but I am interested in a test that is valid only for primes. S((35-1)/2) is divisible by 35 but that is not the first term divisible by 35. Only primes seem to meet the more restricted criteria, i.e. have no term divisible by P prior to S((P-1)/2).
The first two Ramsey primes are 11 and 13 which I call a Ramsey Twin. The largest Ramsey Twin under 1 million is (998651, 998653).
Any thoughts are welcome.
Edit So far about 5 in 13 primes are Ramsey Primes so my test has limited value unless it can be proven that only primes can meet the test. Any way to prove this?
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