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#1
Determine the least possible value of the largest term in an arithmetic progression of seven distinct primes.

Im not quite sure what i have to do
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#2
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1 month ago
#3
(Original post by 5555sasrsr)
Determine the least possible value of the largest term in an arithmetic progression of seven distinct primes.

Im not quite sure what i have to do
Primes have a somewhat random distribution if you look at a lot of them, meaning that they can sometimes occur frequently and other times very sparsely as you walk down the natural numbers.

Sometimes these primes occur and form some sort of arithmetic progression for a short while until they do something different. E.g. {3,5,7} form an arithmetic progression but if you add the common difference of 2 onto 7 then the next term would be 9 which is not prime, so the pattern quickly breaks down here.

What you are interested in, as you begin from 2 going up, is indeed finding the first occurance of when you have seven primes in an arithmetic progression. In this case, the largest of these terms will correspond to the least possible value of such a sequence because it may be that somewhere down the number line you get such an arithmetic progression again, except the largest number out of these future progressions will not be the 'least possible' one.
Last edited by RDKGames; 1 month ago
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#4
(Original post by RDKGames)
Primes have a somewhat random distribution if you look at a lot of them, meaning that they can sometimes occur frequently and other times very sparsely as you walk down the natural numbers.

Sometimes these primes occur and form some sort of arithmetic progression for a short while until they do something different. E.g. {3,5,7} form an arithmetic progression but if you add the common difference of 2 onto 7 then the next term would be 9 which is not prime, so the pattern quickly breaks down here.

What you are interested in, as you begin from 2 going up, is indeed finding the first occurance of when you have seven primes in an arithmetic progression. In this case, the largest of these terms will correspond to the least possible value of such a sequence because it may be that somewhere down the number line you get such an arithmetic progression again, except the largest number out of these future progressions will not be the 'least possible' one.
thank you for the help.
So the sequence is in the form p,p+k,p+2k,..,p+6k
if p is a prime and i add 2, or a multiple of two, every other number would be divisible by 2. So the common difference cannot be a multiple of 2. That's all i got up to.
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1 month ago
#5
(Original post by 5555sasrsr)
thank you for the help.
So the sequence is in the form p,p+k,p+2k,..,p+6k
if p is a prime and i add 2, or a multiple of two, every other number would be divisible by 2. So the common difference cannot be a multiple of 2. That's all i got up to.
The primes must be odd so the differences must be even (a multiple of 2).
Just write down a few example sequences?
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