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Old 2017-10-17, 19:53   #1
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Default sets of 3 primes

Hi all,

See this webpage regarding sets of 3 primes.

here

All primes greater than 2 are odd. Similarly all primes greater than 3 are not divisible by 3.

For what it's worth.

Matt
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Old 2017-10-17, 22:48   #2
science_man_88
 
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"Forget I exist"
Jul 2009
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Quote:
Originally Posted by MattcAnderson View Post
Hi all,

See this webpage regarding sets of 3 primes.

here

All primes greater than 2 are odd. Similarly all primes greater than 3 are not divisible by 3.

For what it's worth.

Matt
seems to be missing the word consecutive see: http://mathworld.wolfram.com/PrimeConstellation.html
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Old 2017-10-17, 23:16   #3
danaj
 
"Dana Jacobsen"
Feb 2011
Bangkok, TH

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MathWorld is, not surprisingly, not quite right. They mean to say consecutive primes, as "consecutive numbers" is obviously wrong.

The OEIS Wiki has a better page than Mathworld:

https://oeis.org/wiki/Prime_constellations

It separates the idea of a cluster from a constellation. Matt's page starts by talking about the standard triplets but then notes we can also find 3-clusters. These are not consecutive primes.

Code:
# replace ... by your list of a,b,... for p,p+a,p+b,...
# perl -Mntheory=:all -E 'say for sieve_prime_cluster(<from>,<to>, ...);
# e.g. one of Matt's clusters:'
perl -Mntheory=:all -E 'say for sieve_prime_cluster(0,1000,102,246);'

# or this random meaningless one:
perl -Mntheory=:all -E 'say for sieve_prime_cluster(0,1e6, 102,246,384,512,770,896);'
The isprime methods are easy to program in a lot of languages (trivial in Pari/GP for instance). The method in the Perl module finds admissable residues, sieves them, then does final primality tests on the remainders. It's fairly fast for large clusters. It is certainly not unique or the first to do it.
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Old 2017-10-18, 00:24   #4
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
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Hi all,

Thanks for the good post Dana. I appreciate it.

Regards,
Matt
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