Prime tuples

[ryzenmulti]

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
https://www.alpertron.com.ar/ECM.HTM

Got any good leads on hunting primes? I'd be keen to hear them.