Find a sequence of 7 consecutive primes











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Find a sequence of 7 consecutive primes, such that these primes have to have the same "gap" in between them. So far I have been doing this in a brute force way, by looking at a list of all the primes and trying different combinations without much luck. Is there a more sophisticated way of doing this?






number-theory prime-numbers







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  • 3




    Note that the common difference will have to be divisible by $2times 3times 5times 7=210$ in order to avoid divisibility by $2,3,5,7$.
    – Mark Bennet
    Nov 11 '14 at 18:39






  • 1




    First, start simple: can you see why a gap of $2$ between primes won't work? Once you see that, you can ask yourself why a gap of $6=2cdot 3$ won't work, and by continuing in this approach you should be able to find the minimum gap that you can use.
    – Steven Stadnicki
    Nov 11 '14 at 18:40






  • 1




    You can look up examples.
    – Henning Makholm
    Nov 11 '14 at 18:42






  • 2




    And this usenet post claims that the smallest known (as of 10 years ago) example is $149143516628800164802930723713131 + 210n$.
    – Henning Makholm
    Nov 11 '14 at 18:46






  • 1




    @DietrichBurde: Those may be primes, but they are not consecutive primes.
    – Henning Makholm
    Nov 11 '14 at 18:46















up vote
2
down vote

favorite
1












Find a sequence of 7 consecutive primes, such that these primes have to have the same "gap" in between them. So far I have been doing this in a brute force way, by looking at a list of all the primes and trying different combinations without much luck. Is there a more sophisticated way of doing this?






number-theory prime-numbers







share|cite|improve this question




















  • 3




    Note that the common difference will have to be divisible by $2times 3times 5times 7=210$ in order to avoid divisibility by $2,3,5,7$.
    – Mark Bennet
    Nov 11 '14 at 18:39






  • 1




    First, start simple: can you see why a gap of $2$ between primes won't work? Once you see that, you can ask yourself why a gap of $6=2cdot 3$ won't work, and by continuing in this approach you should be able to find the minimum gap that you can use.
    – Steven Stadnicki
    Nov 11 '14 at 18:40






  • 1




    You can look up examples.
    – Henning Makholm
    Nov 11 '14 at 18:42






  • 2




    And this usenet post claims that the smallest known (as of 10 years ago) example is $149143516628800164802930723713131 + 210n$.
    – Henning Makholm
    Nov 11 '14 at 18:46






  • 1




    @DietrichBurde: Those may be primes, but they are not consecutive primes.
    – Henning Makholm
    Nov 11 '14 at 18:46













up vote
2
down vote

favorite
1









up vote
2
down vote

favorite
1






1





Find a sequence of 7 consecutive primes, such that these primes have to have the same "gap" in between them. So far I have been doing this in a brute force way, by looking at a list of all the primes and trying different combinations without much luck. Is there a more sophisticated way of doing this?






number-theory prime-numbers







share|cite|improve this question















Find a sequence of 7 consecutive primes, such that these primes have to have the same "gap" in between them. So far I have been doing this in a brute force way, by looking at a list of all the primes and trying different combinations without much luck. Is there a more sophisticated way of doing this?






number-theory prime-numbers




number-theory prime-numbers






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 21 at 15:02









Klangen

1,32811130




1,32811130










asked Nov 11 '14 at 18:35









Math Major

1,06021437




1,06021437








  • 3




    Note that the common difference will have to be divisible by $2times 3times 5times 7=210$ in order to avoid divisibility by $2,3,5,7$.
    – Mark Bennet
    Nov 11 '14 at 18:39






  • 1




    First, start simple: can you see why a gap of $2$ between primes won't work? Once you see that, you can ask yourself why a gap of $6=2cdot 3$ won't work, and by continuing in this approach you should be able to find the minimum gap that you can use.
    – Steven Stadnicki
    Nov 11 '14 at 18:40






  • 1




    You can look up examples.
    – Henning Makholm
    Nov 11 '14 at 18:42






  • 2




    And this usenet post claims that the smallest known (as of 10 years ago) example is $149143516628800164802930723713131 + 210n$.
    – Henning Makholm
    Nov 11 '14 at 18:46






  • 1




    @DietrichBurde: Those may be primes, but they are not consecutive primes.
    – Henning Makholm
    Nov 11 '14 at 18:46














  • 3




    Note that the common difference will have to be divisible by $2times 3times 5times 7=210$ in order to avoid divisibility by $2,3,5,7$.
    – Mark Bennet
    Nov 11 '14 at 18:39






  • 1




    First, start simple: can you see why a gap of $2$ between primes won't work? Once you see that, you can ask yourself why a gap of $6=2cdot 3$ won't work, and by continuing in this approach you should be able to find the minimum gap that you can use.
    – Steven Stadnicki
    Nov 11 '14 at 18:40






  • 1




    You can look up examples.
    – Henning Makholm
    Nov 11 '14 at 18:42






  • 2




    And this usenet post claims that the smallest known (as of 10 years ago) example is $149143516628800164802930723713131 + 210n$.
    – Henning Makholm
    Nov 11 '14 at 18:46






  • 1




    @DietrichBurde: Those may be primes, but they are not consecutive primes.
    – Henning Makholm
    Nov 11 '14 at 18:46








3




3




Note that the common difference will have to be divisible by $2times 3times 5times 7=210$ in order to avoid divisibility by $2,3,5,7$.
– Mark Bennet
Nov 11 '14 at 18:39




Note that the common difference will have to be divisible by $2times 3times 5times 7=210$ in order to avoid divisibility by $2,3,5,7$.
– Mark Bennet
Nov 11 '14 at 18:39




1




1




First, start simple: can you see why a gap of $2$ between primes won't work? Once you see that, you can ask yourself why a gap of $6=2cdot 3$ won't work, and by continuing in this approach you should be able to find the minimum gap that you can use.
– Steven Stadnicki
Nov 11 '14 at 18:40




First, start simple: can you see why a gap of $2$ between primes won't work? Once you see that, you can ask yourself why a gap of $6=2cdot 3$ won't work, and by continuing in this approach you should be able to find the minimum gap that you can use.
– Steven Stadnicki
Nov 11 '14 at 18:40




1




1




You can look up examples.
– Henning Makholm
Nov 11 '14 at 18:42




You can look up examples.
– Henning Makholm
Nov 11 '14 at 18:42




2




2




And this usenet post claims that the smallest known (as of 10 years ago) example is $149143516628800164802930723713131 + 210n$.
– Henning Makholm
Nov 11 '14 at 18:46




And this usenet post claims that the smallest known (as of 10 years ago) example is $149143516628800164802930723713131 + 210n$.
– Henning Makholm
Nov 11 '14 at 18:46




1




1




@DietrichBurde: Those may be primes, but they are not consecutive primes.
– Henning Makholm
Nov 11 '14 at 18:46




@DietrichBurde: Those may be primes, but they are not consecutive primes.
– Henning Makholm
Nov 11 '14 at 18:46










1 Answer
1






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oldest

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up vote
3
down vote



accepted










http://primerecords.dk/cpap.htm lists largest and smallest known examples of consecutive primes in arithmetic progression of a given length.



The first known sequence is apparently $19252884016114523644357039386451+210n$, but is not known to be the first.






share|cite|improve this answer























  • So for simplicity I just want to pick a small one, but I just want to make sure I am reading the chart correctly, so I look at CPAP-k with a k of 7 right? So I chose: 1205967 · 61# + x32a + 210n but I don't understand what the a and # are symbolizing?
    – Math Major
    Nov 11 '14 at 18:55






  • 1




    @MathMajor: $61#$ is a primorial, that is, the product of all primes up to $61$. And $x_{32a}$ is a particular 32-digit number that is listed further down that page. The smallest known CPAP-7 base is quoted explicitly slightly above the "smallest known CPAP-k" table, after the words "The smallest known is 32 digits".
    – Henning Makholm
    Nov 11 '14 at 19:02












  • Oh ok, so primorial is like a factorial, but exclusively for the prime numberS?
    – Math Major
    Nov 11 '14 at 19:04






  • 1




    @MathMajor: Yes.
    – Henning Makholm
    Nov 11 '14 at 19:05











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1 Answer
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1 Answer
1






active

oldest

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active

oldest

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active

oldest

votes








up vote
3
down vote



accepted










http://primerecords.dk/cpap.htm lists largest and smallest known examples of consecutive primes in arithmetic progression of a given length.



The first known sequence is apparently $19252884016114523644357039386451+210n$, but is not known to be the first.






share|cite|improve this answer























  • So for simplicity I just want to pick a small one, but I just want to make sure I am reading the chart correctly, so I look at CPAP-k with a k of 7 right? So I chose: 1205967 · 61# + x32a + 210n but I don't understand what the a and # are symbolizing?
    – Math Major
    Nov 11 '14 at 18:55






  • 1




    @MathMajor: $61#$ is a primorial, that is, the product of all primes up to $61$. And $x_{32a}$ is a particular 32-digit number that is listed further down that page. The smallest known CPAP-7 base is quoted explicitly slightly above the "smallest known CPAP-k" table, after the words "The smallest known is 32 digits".
    – Henning Makholm
    Nov 11 '14 at 19:02












  • Oh ok, so primorial is like a factorial, but exclusively for the prime numberS?
    – Math Major
    Nov 11 '14 at 19:04






  • 1




    @MathMajor: Yes.
    – Henning Makholm
    Nov 11 '14 at 19:05















up vote
3
down vote



accepted










http://primerecords.dk/cpap.htm lists largest and smallest known examples of consecutive primes in arithmetic progression of a given length.



The first known sequence is apparently $19252884016114523644357039386451+210n$, but is not known to be the first.






share|cite|improve this answer























  • So for simplicity I just want to pick a small one, but I just want to make sure I am reading the chart correctly, so I look at CPAP-k with a k of 7 right? So I chose: 1205967 · 61# + x32a + 210n but I don't understand what the a and # are symbolizing?
    – Math Major
    Nov 11 '14 at 18:55






  • 1




    @MathMajor: $61#$ is a primorial, that is, the product of all primes up to $61$. And $x_{32a}$ is a particular 32-digit number that is listed further down that page. The smallest known CPAP-7 base is quoted explicitly slightly above the "smallest known CPAP-k" table, after the words "The smallest known is 32 digits".
    – Henning Makholm
    Nov 11 '14 at 19:02












  • Oh ok, so primorial is like a factorial, but exclusively for the prime numberS?
    – Math Major
    Nov 11 '14 at 19:04






  • 1




    @MathMajor: Yes.
    – Henning Makholm
    Nov 11 '14 at 19:05













up vote
3
down vote



accepted







up vote
3
down vote



accepted






http://primerecords.dk/cpap.htm lists largest and smallest known examples of consecutive primes in arithmetic progression of a given length.



The first known sequence is apparently $19252884016114523644357039386451+210n$, but is not known to be the first.






share|cite|improve this answer














http://primerecords.dk/cpap.htm lists largest and smallest known examples of consecutive primes in arithmetic progression of a given length.



The first known sequence is apparently $19252884016114523644357039386451+210n$, but is not known to be the first.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Nov 11 '14 at 19:05

























answered Nov 11 '14 at 18:51









Henning Makholm

236k16300534




236k16300534












  • So for simplicity I just want to pick a small one, but I just want to make sure I am reading the chart correctly, so I look at CPAP-k with a k of 7 right? So I chose: 1205967 · 61# + x32a + 210n but I don't understand what the a and # are symbolizing?
    – Math Major
    Nov 11 '14 at 18:55






  • 1




    @MathMajor: $61#$ is a primorial, that is, the product of all primes up to $61$. And $x_{32a}$ is a particular 32-digit number that is listed further down that page. The smallest known CPAP-7 base is quoted explicitly slightly above the "smallest known CPAP-k" table, after the words "The smallest known is 32 digits".
    – Henning Makholm
    Nov 11 '14 at 19:02












  • Oh ok, so primorial is like a factorial, but exclusively for the prime numberS?
    – Math Major
    Nov 11 '14 at 19:04






  • 1




    @MathMajor: Yes.
    – Henning Makholm
    Nov 11 '14 at 19:05


















  • So for simplicity I just want to pick a small one, but I just want to make sure I am reading the chart correctly, so I look at CPAP-k with a k of 7 right? So I chose: 1205967 · 61# + x32a + 210n but I don't understand what the a and # are symbolizing?
    – Math Major
    Nov 11 '14 at 18:55






  • 1




    @MathMajor: $61#$ is a primorial, that is, the product of all primes up to $61$. And $x_{32a}$ is a particular 32-digit number that is listed further down that page. The smallest known CPAP-7 base is quoted explicitly slightly above the "smallest known CPAP-k" table, after the words "The smallest known is 32 digits".
    – Henning Makholm
    Nov 11 '14 at 19:02












  • Oh ok, so primorial is like a factorial, but exclusively for the prime numberS?
    – Math Major
    Nov 11 '14 at 19:04






  • 1




    @MathMajor: Yes.
    – Henning Makholm
    Nov 11 '14 at 19:05
















So for simplicity I just want to pick a small one, but I just want to make sure I am reading the chart correctly, so I look at CPAP-k with a k of 7 right? So I chose: 1205967 · 61# + x32a + 210n but I don't understand what the a and # are symbolizing?
– Math Major
Nov 11 '14 at 18:55




So for simplicity I just want to pick a small one, but I just want to make sure I am reading the chart correctly, so I look at CPAP-k with a k of 7 right? So I chose: 1205967 · 61# + x32a + 210n but I don't understand what the a and # are symbolizing?
– Math Major
Nov 11 '14 at 18:55




1




1




@MathMajor: $61#$ is a primorial, that is, the product of all primes up to $61$. And $x_{32a}$ is a particular 32-digit number that is listed further down that page. The smallest known CPAP-7 base is quoted explicitly slightly above the "smallest known CPAP-k" table, after the words "The smallest known is 32 digits".
– Henning Makholm
Nov 11 '14 at 19:02






@MathMajor: $61#$ is a primorial, that is, the product of all primes up to $61$. And $x_{32a}$ is a particular 32-digit number that is listed further down that page. The smallest known CPAP-7 base is quoted explicitly slightly above the "smallest known CPAP-k" table, after the words "The smallest known is 32 digits".
– Henning Makholm
Nov 11 '14 at 19:02














Oh ok, so primorial is like a factorial, but exclusively for the prime numberS?
– Math Major
Nov 11 '14 at 19:04




Oh ok, so primorial is like a factorial, but exclusively for the prime numberS?
– Math Major
Nov 11 '14 at 19:04




1




1




@MathMajor: Yes.
– Henning Makholm
Nov 11 '14 at 19:05




@MathMajor: Yes.
– Henning Makholm
Nov 11 '14 at 19:05


















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