Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , for instance 5, ), an even number divisible by 3 and 2, and Group 2 for all primes that are after ζ (such that , for instance 7), then we find a simple function: for each prime in each group, , where n is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a μ value for each prime. The μ value can be attributed to every prime greater than 7. Thus for Group 1, and . Using this formula, all the primes appear for , where μ is any natural number.
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![](\"https://html.scirp.org//file/5302399-rId13.svg?20240416020453\")
, for instance 5, ![](\"https://html.scirp.org//file/5302399-rId15.svg?20240416020453\")
), an even number divisible by 3 and 2, and Group 2 for all primes that are after ζ (such that ![](\"https://html.scirp.org//file/5302399-rId17.svg?20240416020453\")
, for instance 7), then we find a simple function: for each prime in each group, ![](\"https://html.scirp.org//file/5302399-rId19.svg?20240416020453\")
, where n is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a μ value for each prime. The μ value can be attributed to every prime greater than 7. Thus ![](\"https://html.scirp.org//file/5302399-rId21.svg?20240416020453\")
for Group 1, and ![](\"https://html.scirp.org//file/5302399-rId23.svg?20240416020453\")
. Using this formula, all the primes appear for ![](\"https://html.scirp.org//file/5302399-rId25.svg?20240416020453\")
, where μ is any natural number.
