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Prime tuples

Started by ryzenmulti, May 17, 2023, 06:29:55 AM

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All this boinc investment has created an unhealthy interest in prime numbers. Every prime number in existence must be odd, and end in 1, 3, 7 or 9. More interesting are the twin primes. These are 'prime tuples' and are not the twins I was planning on spending long days with. The twin prime conjecture says there are infinitely many twin primes that differ by 2 (e.g. (10000079999771, 10000079999773). You can harvest hundreds of these less than 500 digits in a matter of seconds. At 4000 digits it gets exponentially harder - less than 1 in a million on average.

Then there are quad primes (4 tuples) are each of the 1/3/7/9 in the same decile - within 10 of each other. e.g. (299899421, 299899423, 299899427, 299899429). Amazeballs hey? But wait, there's more! there are 5,6,7 8 tuples. What are the odds? Imagine wandering along the number line at 4150 digits and coming across 4 consecutive prime numbers - I can tell you much much less than 1 in a billion. There are infinitely many of them, they just get further and further apart on the average.

Anyone keen on developing a distracting hobby in prime numbers might find these useful -
github->primesieve (windows and linux) - extremely fast, very flexible, does up to 2^64 (18 digits)
python->primefac (python -m pip install primefac)
python by default limits integers to 4300 digits; this limit can be removed if you have enough spare time
want to test primes with 10,000 digits? no problem!, go here

Got any good leads on hunting primes? I'd be keen to hear them.
The further back you look, the further forward you can see.

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Home cooked twin primes using python ... it started out with 256 digits of pi and eulers number ... and has ended with
(6*(3358638*(5^6137)+177))-1 ,4297 digits, is prime
(6*(3358638*(5^6137)+177))+1 ,4297 digits, is prime