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Message boards :
AP26 - AP27 Search :
AP Prime Numbers
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Hi,
i'm interested if prime numbers of AP findings are worth to be reported, and if they can displayed in the 'Top Prime Finders' table.
I'm also interested to know how long they are (how many digits in decimal), and also how big is the gap between the primes in a row (maybe i can calculate myself).
Michael
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 Michael Goetz Volunteer moderator
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Hi,
i'm interested if prime numbers of AP findings are worth to be reported, and if they can displayed in the 'Top Prime Finders' table.
I'm also interested to know how long they are (how many digits in decimal), and also how big is the gap between the primes in a row (maybe i can calculate myself).
Michael
The prime numbers themselves are not particularly interesting. They're very small. It's the fact that they form a long sequence of prime numbers that makes them interesting.
For example, the first prime number in the AP26 discovered recently is 149836681069944461. That's 18 digits. That's about 388 thousand digits too small to qualify for the Top 5000 primes.
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My lucky number is 75898524288+1 | |
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Hi Michael,
thank you for the information.
I didn't thought that they are so small.
Michael | |
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Curiosity, does anybody know what happens primenumberwise in between the primes in the AP series? Does AP series overlap? | |
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Curiosity, does anybody know what happens primenumberwise in between the primes in the AP series? Does AP series overlap?
There will almost always be other primes in between the primes in an AP series.
Finding an instance where that is not the case, is much harder; it is called a CPAP with the terminology used e.g. in http://primerecords.dk/.
For your other question, yes, AP series will overlap in general. For example {31, 37, 43} is an AP, and {29, 41, 53} is an AP as well.
/JeppeSN
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compositeVolunteer tester
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AP series will overlap in general. For example {31, 37, 43} is an AP, and {29, 41, 53} is an AP as well.
Also, AP series may have primes in common. For example {31, 37, 43} and {19, 31, 43}. | |
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AP series will overlap in general. For example {31, 37, 43} is an AP, and {29, 41, 53} is an AP as well.
Also, AP series may have primes in common. For example {31, 37, 43} and {19, 31, 43}.
And you expect each odd prime p to be a member of infinitely many arithmetic progressions of primes.
However, for a fixed prime p, the length of the APs it can be a member of is bounded. For example, for p=31, no AP of primes (one of which is 31) can have a length of 32 (or more), because then one other member of the AP would be a multiple of 31, and hence composite.
/JeppeSN | |
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JaySend message
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Are AP series generally interesting mathematical oddities only, or is there an application where they can be put to use in the real world? | |
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Are AP series generally interesting mathematical oddities only, or is there an application where they can be put to use in the real world?
Mathematics is the real world, you know. Everything else is just impure approximations to it.
But I do not think there are any practical applications. The main result (2004) is that they come in all lengths (Green–Tao, free access to full article The primes contain arbitrarily long arithmetic progressions (2008)).
/JeppeSN | |
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JaySend message
Joined: 27 Feb 10
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Mathematics is the real world, you know. Everything else is just impure approximations to it.
Never heard it that way before, but I like it.
But I do not think there are any practical applications.
Thanks, for some reason, in my head, I seem to get them crossed with the optimal Golomb rulers that distributed.net is working on. | |
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