Is there a way to predict the difference between two primes based on previous differences
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0
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If we know the difference between for instance
$5-3=2$ and if we also know the difference between
$7-5=2$, can we then predict the difference between
$X-7=$? Where $X = 11$.
Is there an equation/algorithm that can predict the difference without knowing $X$? Based on sums or something?
prime-numbers
edited 2 days ago
Flermat
1,27911129
asked Jul 27 '17 at 16:27
Simon
435
add a comment |
up vote
0
down vote
favorite
If we know the difference between for instance
$5-3=2$ and if we also know the difference between
$7-5=2$, can we then predict the difference between
$X-7=$? Where $X = 11$.
Is there an equation/algorithm that can predict the difference without knowing $X$? Based on sums or something?
prime-numbers
edited 2 days ago
Flermat
1,27911129
asked Jul 27 '17 at 16:27
Simon
435
not really but we can prove that say 5 consecutive differences can't all be the same ( unless they are 5 ( impossible in the odd primes)), in any 5 values at least 2 must share their remainders when dividing by 5. this is a straight application of the pigeonhole principle to primes in arithmetic progressions.
– user451844
Jul 27 '17 at 16:38
If the Twin Prime Conjecture mathworld.wolfram.com/TwinPrimeConjecture.html is false, then we can say there is a number M so that $p_{i+1}-p_i$>2 , where $p_i$ is the $i_th$ prime.
– gary
Jul 27 '17 at 16:42
For any sequence $a_1,a_2,a_3,cdots$ of which $a_1$ is known, knowing the sequence of differences $a_2-a_1, a_3-a_2, a_4-a_3,cdots$ is exactly the same thing as knowing the sequence itself.
– user228113
Jul 27 '17 at 16:46
we know all primes greater than 3 are 1 or 5 remainder on division by 6 ...
– user451844
Jul 27 '17 at 17:08
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If we know the difference between for instance
$5-3=2$ and if we also know the difference between
$7-5=2$, can we then predict the difference between
$X-7=$? Where $X = 11$.
Is there an equation/algorithm that can predict the difference without knowing $X$? Based on sums or something?
prime-numbers
edited 2 days ago
Flermat
1,27911129
asked Jul 27 '17 at 16:27
Simon
435
If we know the difference between for instance
$5-3=2$ and if we also know the difference between
$7-5=2$, can we then predict the difference between
$X-7=$? Where $X = 11$.
Is there an equation/algorithm that can predict the difference without knowing $X$? Based on sums or something?
prime-numbers
prime-numbers
edited 2 days ago
Flermat
1,27911129
asked Jul 27 '17 at 16:27
Simon
435
edited 2 days ago
Flermat
1,27911129
asked Jul 27 '17 at 16:27
Simon
435
edited 2 days ago
Flermat
1,27911129
edited 2 days ago
Flermat
1,27911129
edited 2 days ago
Flermat
1,27911129
1,27911129
asked Jul 27 '17 at 16:27
Simon
435
asked Jul 27 '17 at 16:27
Simon
435
asked Jul 27 '17 at 16:27
Simon
435
435
not really but we can prove that say 5 consecutive differences can't all be the same ( unless they are 5 ( impossible in the odd primes)), in any 5 values at least 2 must share their remainders when dividing by 5. this is a straight application of the pigeonhole principle to primes in arithmetic progressions.
– user451844
Jul 27 '17 at 16:38
If the Twin Prime Conjecture mathworld.wolfram.com/TwinPrimeConjecture.html is false, then we can say there is a number M so that $p_{i+1}-p_i$>2 , where $p_i$ is the $i_th$ prime.
– gary
Jul 27 '17 at 16:42
For any sequence $a_1,a_2,a_3,cdots$ of which $a_1$ is known, knowing the sequence of differences $a_2-a_1, a_3-a_2, a_4-a_3,cdots$ is exactly the same thing as knowing the sequence itself.
– user228113
Jul 27 '17 at 16:46
we know all primes greater than 3 are 1 or 5 remainder on division by 6 ...
– user451844
Jul 27 '17 at 17:08
add a comment |
not really but we can prove that say 5 consecutive differences can't all be the same ( unless they are 5 ( impossible in the odd primes)), in any 5 values at least 2 must share their remainders when dividing by 5. this is a straight application of the pigeonhole principle to primes in arithmetic progressions.
– user451844
Jul 27 '17 at 16:38
If the Twin Prime Conjecture mathworld.wolfram.com/TwinPrimeConjecture.html is false, then we can say there is a number M so that $p_{i+1}-p_i$>2 , where $p_i$ is the $i_th$ prime.
– gary
Jul 27 '17 at 16:42
For any sequence $a_1,a_2,a_3,cdots$ of which $a_1$ is known, knowing the sequence of differences $a_2-a_1, a_3-a_2, a_4-a_3,cdots$ is exactly the same thing as knowing the sequence itself.
– user228113
Jul 27 '17 at 16:46
we know all primes greater than 3 are 1 or 5 remainder on division by 6 ...
– user451844
Jul 27 '17 at 17:08
not really but we can prove that say 5 consecutive differences can't all be the same ( unless they are 5 ( impossible in the odd primes)), in any 5 values at least 2 must share their remainders when dividing by 5. this is a straight application of the pigeonhole principle to primes in arithmetic progressions.
– user451844
Jul 27 '17 at 16:38
not really but we can prove that say 5 consecutive differences can't all be the same ( unless they are 5 ( impossible in the odd primes)), in any 5 values at least 2 must share their remainders when dividing by 5. this is a straight application of the pigeonhole principle to primes in arithmetic progressions.
– user451844
Jul 27 '17 at 16:38
If the Twin Prime Conjecture mathworld.wolfram.com/TwinPrimeConjecture.html is false, then we can say there is a number M so that $p_{i+1}-p_i$>2 , where $p_i$ is the $i_th$ prime.
– gary
Jul 27 '17 at 16:42
If the Twin Prime Conjecture mathworld.wolfram.com/TwinPrimeConjecture.html is false, then we can say there is a number M so that $p_{i+1}-p_i$>2 , where $p_i$ is the $i_th$ prime.
– gary
Jul 27 '17 at 16:42
For any sequence $a_1,a_2,a_3,cdots$ of which $a_1$ is known, knowing the sequence of differences $a_2-a_1, a_3-a_2, a_4-a_3,cdots$ is exactly the same thing as knowing the sequence itself.
– user228113
Jul 27 '17 at 16:46
For any sequence $a_1,a_2,a_3,cdots$ of which $a_1$ is known, knowing the sequence of differences $a_2-a_1, a_3-a_2, a_4-a_3,cdots$ is exactly the same thing as knowing the sequence itself.
– user228113
Jul 27 '17 at 16:46
we know all primes greater than 3 are 1 or 5 remainder on division by 6 ...
– user451844
Jul 27 '17 at 17:08
we know all primes greater than 3 are 1 or 5 remainder on division by 6 ...
– user451844
Jul 27 '17 at 17:08
add a comment |
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not really but we can prove that say 5 consecutive differences can't all be the same ( unless they are 5 ( impossible in the odd primes)), in any 5 values at least 2 must share their remainders when dividing by 5. this is a straight application of the pigeonhole principle to primes in arithmetic progressions.
– user451844
Jul 27 '17 at 16:38
If the Twin Prime Conjecture mathworld.wolfram.com/TwinPrimeConjecture.html is false, then we can say there is a number M so that $p_{i+1}-p_i$>2 , where $p_i$ is the $i_th$ prime.
– gary
Jul 27 '17 at 16:42
For any sequence $a_1,a_2,a_3,cdots$ of which $a_1$ is known, knowing the sequence of differences $a_2-a_1, a_3-a_2, a_4-a_3,cdots$ is exactly the same thing as knowing the sequence itself.
– user228113
Jul 27 '17 at 16:46
we know all primes greater than 3 are 1 or 5 remainder on division by 6 ...
– user451844
Jul 27 '17 at 17:08