Schinzel-Sierpinski conjecture: Difference between revisions

Latest revision as of 01:26, 3 July 2012

The name Schinzel-Sierpinski conjecture is used for two related conjectures:

For any positive rational number $r$ , there exist prime numbers $p,q$ such that $r={\frac {p+1}{q+1}}$ . A stronger version of the conjecture asserts that there are infinitely many such pairs of prime numbers.
For any positive rational number $r$ , there exist prime numbers $p,q$ such that $r={\frac {p-1}{q-1}}$ . A stronger version of the conjecture asserts that there are infinitely many such pairs of prime numbers.

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 The name '''Schinzel-Sierpinski conjecture''' is used for two related conjectures:
-* For any positive rational number <math>r</math>, there exist [[prime number]]s <math>p,q</math> such that <math>r = \frac{p + 1}{q + 1}</math> (in fact, we would expect there to be infinitely many such prime pairs).
+* For any positive rational number <math>r</math>, there exist [[prime number]]s <math>p,q</math> such that <math>r = \frac{p + 1}{q + 1}</math>. A stronger version of the conjecture asserts that there are infinitely many such pairs of prime numbers.
-* For any positive rational number <math>r</math>, there exist [[prime number]]s <math>p,q</math> such that <math>r = \frac{p - 1}{q - 1}</math> (in fact, we would expect there to be infinitely many such prime pairs).
+* For any positive rational number <math>r</math>, there exist [[prime number]]s <math>p,q</math> such that <math>r = \frac{p - 1}{q - 1}</math>. A stronger version of the conjecture asserts that there are infinitely many such pairs of prime numbers.
 ==References==
 * [http://oeis.org/wiki/User%3APeter_Luschny/SchinzelSierpinskiConjectureAndCalkinWilfTree Computations related to the conjecture]