Sierpiński conjecture

In 1960 Wacław Sierpiński (1882-1969) proved the following interesting result:

Theorem:There exist infinitely many odd integers $k$ such that $k2^{n}+1$ is composite for every integer $n\\geq 1$ .

A multiplier $k$ with this propertyis called a Sierpiński number (http://planetmath.org/SierpinskiNumbers).The Sierpiński problem consists indetermining the smallest Sierpiński number.In 1962, John Selfridge discovered the Sierpiński number $k=78557$ ,which is now believed to be in fact the smallest such number.

Conjecture:The integer $k=78557$ is the smallest Sierpiński number.

To prove the conjecture, it would be sufficient to exhibita prime $k2^{n}+1$ for each $k<78557$ .

单词	SierpinskiConjecture
释义	Sierpiński conjecture In 1960 Wacław Sierpiński (1882-1969) proved the following interesting result: Theorem:There exist infinitely many odd integers $k$ such that $k2^{n}+1$ is composite for every integer $n\\geq 1$ . A multiplier $k$ with this propertyis called a Sierpiński number (http://planetmath.org/SierpinskiNumbers).The Sierpiński problem consists indetermining the smallest Sierpiński number.In 1962, John Selfridge discovered the Sierpiński number $k=78557$ ,which is now believed to be in fact the smallest such number. Conjecture:The integer $k=78557$ is the smallest Sierpiński number. To prove the conjecture, it would be sufficient to exhibita prime $k2^{n}+1$ for each $k<78557$ .
随便看	subcoalgebras and coideals Subcommutative subcommutative SubdifferentiableMapping subdifferentiable mapping SubdirectlyIrreducibleRing subdirectly irreducible ring SubdirectProductOfAlgebraicSystems subdirect product of algebraic systems SubdirectProductOfGroups subdirect product of groups SubdirectProductOfRings subdirect product of rings Subdivision subdivision Subfield subfield SubfieldCriterion subfield criterion Subformula subformula Subfunction subfunction SubgoupsOfLocallyCyclicGroupsAreLocallyCyclic subgoups of locally cyclic groups are locally cyclic