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edited Jul 25 2011 at 20:26 |
Melvyn Nathanson, in his book Elementary Methods in Number Theory (Chapter 8: Prime Numbers) states the following:
- A conjecture of Schinzel and Sierpinski asserts that every positive rational number $x$ can be represented as a quotient of shifted primes, that $x=\frac{p+1}{q+1}$ for primes $p$ and $q$. It is known that the set of shifted primes, generates a subgroup of the multiplicative group of rational numbers of index at most $3$.
I would like to know what progress has been made regarding this problem and why is this conjecture important. Since it generates a subgroup, does the subgroup which it generates have any special properties?
I had actually posed a problem which asks us to prove that given any interval $(a,b)$ there is a rational of the form $\frac{p}{q}$($p,q$ \frac{p}{q}$ ($p,q$ primes) which lies inside $(a,b)$. Does, this problem have any connections with the actual conjecture?
I had actually posed this question on MATH.SE (Link : http://math.stackexchange.com/questions/18352/a-conjecture-of-schinzel-and-sierpinski ).
I did get a decent answer from Andreis Caicedo, but i would like to have more opinions of Mathematicians from this community.
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edited Feb 11 2011 at 15:56 |
Melvyn Nathanson, in his book Elementary Methods in Number Theory (Chapter 8: Prime Numbers) states the following:
- A conjecture of Schinzel and Sierpinski asserts that every positive rational number $x$ can be represented as a quotient of shifted primes, that $x=\frac{p+1}{q+1}$ for primes $p$ and $q$. It is known that the set of shifted primes, generates a subgroup of the multiplicative group of rational numbers of index at most $3$.
I would like to know what progress has been made regarding this problem and why is this conjecture important. Since it generates a subgroup, does the subgroup which it generates have any special properties?
I had actually posed a problem which asks us to prove that given any interval $(a,b)$ there is a rational of the form $\frac{p}{q}$($p,q$ primes) which lies inside $(a,b)$. Does, this problem have any connections with the actual conjecture?
I had actually posed this question on MATH.SE (Link : http://math.stackexchange.com/questions/18352/a-conjecture-of-schinzel-and-sierpinski ).
I did get a decent answer from Andreis Caicedo, but i would like to have more opinions of Mathematicians from this community.
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edited Feb 10 2011 at 16:18 |
Melvyn Nathanson, in his book Elementary Methods in Number Theory (Chapter 8: Prime Numbers) states the following:
- A conjecture of Schinzel and Sierpinski asserts that every positive rational number $x$ can be represented as a quotient of shifted primes, that $x=\frac{p+1}{q+1}$ for primes $p$ and $q$. It is known that the set of shifted primes, generates a subgroup of the multiplicative group of rational numbers of index at most $3$.
Well, i
I would like to know what progress has been made regarding this problem and why is this conjecture important. Since it generates a subgroup, does the subgroup which it generates have any special properties?
I had actually posed a problem which asks us to prove that given any interval $(a,b)$ there is a rational of the form $\frac{p}{q}$($p,q$ primes) which lies inside $(a,b)$. Does, this problem have any connections with the actual conjecture?
I had actually posed this question on MATH.SE (Link : http://math.stackexchange.com/questions/18352/a-conjecture-of-schinzel-and-sierpinski ).
I did get a decent answer from Andreis Caicedo, but i would like to have more opinions of Mathematicians from this community.
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edited Feb 10 2011 at 6:39 |
Melvyn Nathanson, in his book Elementary Methods in Number Theory (Chapter 8: Prime Numbers) states the following:
- A conjecture of Schinzel and Sierpinski asserts that every positive rational number $x$ can be represented as a quotient of shifted primes, that $x=\frac{p+1}{q+1}$ for primes $p$ and $q$. It is known that the set of shifted primes, generates a subgroup of the multiplicative group of rational numbers of index at most $3$.
Well, i would like to know what progress has been made regarding this problem and why is this conjecture important. Since it generates a subgroup, does the subgroup which it generates have any special properties?
I had actually posed a problem which asks us to prove that given any interval $(a,b)$ there is a rational of the form $\frac{p}{q}$($p,q$ primes) which lies inside $(a,b)$. Does, this problem have any connections with the actual conjecture?
I had actually posed this question on MATH.SE (Link : http://math.stackexchange.com/questions/18352/a-conjecture-of-schinzel-and-sierpinski ).
I did get a decent answer from Andreis Caicedo, but i would like to have more opinions of Mathematicians from this community.
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edited Jan 30 2011 at 19:06 |
On a Conjecture of Schnizel Schinzel and Sierpinski
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edited Jan 30 2011 at 18:59 |
Melvyn Nathanson, in his book Elementary Methods in Number Theory (Chapter 8: Prime Number'sNumbers) states the following:
- A conjecture of Schinzel and Sierpinski asserts that every positive rational number $x$ can be represented as a quotient of shifted primes, that $x=\frac{p+1}{q+1}$ for primes $p$ and $q$. It is known that the set of shifted primes, generates a subgroup of the multiplicative group of rational numbers of index at most $3$.
Well, i would like to know what progress has been made regarding this problem and why is this conjecture important. Since it generates a subgroup, does the subgroup which it generates have any special properties?
I had actually posed a problem which asks us to prove that given any interval $(a,b)$ there is a rational of the form $\frac{p}{q}$($p,q$ primes) which lies inside $(a,b)$. Does, this problem have any connections with the actual conjecture?
I had actually posed this question on MATH.SE (Link : http://math.stackexchange.com/questions/18352/a-conjecture-of-schinzel-and-sierpinski ). I did get a decent answer from Andreis Caicedo, but i would like to have more opinions of Mathematicians from this community.
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asked Jan 29 2011 at 19:48 |
On a Conjecture of Schnizel and Sierpinski
Melvyn Nathanson, in his book Methods in Number Theory (Chapter 8: Prime Number's) states the following:
- A conjecture of Schinzel and Sierpinski asserts that every positive rational number $x$ can be represented as a quotient of shifted primes, that $x=\frac{p+1}{q+1}$ for primes $p$ and $q$. It is known that the set of shifted primes, generates a subgroup of the multiplicative group of rational numbers of index at most $3$.
Well, i would like to know what progress has been made regarding this problem and why is this conjecture important. Since it generates a subgroup, does the subgroup which it generates have any special properties?
I had actually posed a problem which asks us to prove that given any interval $(a,b)$ there is a rational of the form $\frac{p}{q}$($p,q$ primes) which lies inside $(a,b)$. Does, this problem have any connections with the actual conjecture?
I had actually posed this question on MATH.SE (Link : http://math.stackexchange.com/questions/18352/a-conjecture-of-schinzel-and-sierpinski ). I did get a decent answer from Andreis Caicedo, but i would like to have more opinions of Mathematicians from this community.
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