table of primes in arithmetic progressions per Dirichlet’s theorem

Dirichlet’s theorem on primes in arithmetic progressions tells us that given the $n$ th prime $p_{n}$ , there are infinitely many primes of the form $mp_{n}+1$ . Obviously, for $p_{1}=2$ , the primes of that form are merely the odd primes. For the other primes, $m$ has to be even, but not much else appears obvious.

The leftmost column of this table gives the $n$ th prime, the second column from the left gives the smallest prime of the form $mp_{n}+1$ , the third column from the left gives the second smallest prime of that form, etc. Apart from the leftmost column, none of the columns contain a sequence in ascending order.

单词	TableOfPrimesInArithmeticProgressionsPerDirichletsTheorem
释义	table of primes in arithmetic progressions per Dirichlet’s theorem Dirichlet’s theorem on primes in arithmetic progressions tells us that given the $n$ th prime $p_{n}$ , there are infinitely many primes of the form $mp_{n}+1$ . Obviously, for $p_{1}=2$ , the primes of that form are merely the odd primes. For the other primes, $m$ has to be even, but not much else appears obvious. The leftmost column of this table gives the $n$ th prime, the second column from the left gives the smallest prime of the form $mp_{n}+1$ , the third column from the left gives the second smallest prime of that form, etc. Apart from the leftmost column, none of the columns contain a sequence in ascending order.
随便看	control system ConvergenceConditionOfInfiniteProduct convergence condition of infinite product ConvergenceCriterionForInfiniteProduct convergence criterion for infinite product ConvergencedivergenceForAnInfiniteProduct convergence/divergence for an infinite product ConvergenceInDistribution convergence in distribution ConvergenceInProbability convergence in probability ConvergenceInProbabilityIsPreservedUnderContinuousTransformations convergence in probability is preserved under continuous transformations ConvergenceInTheMean convergence in the mean ConvergenceOfArithmeticgeometricMean convergence of arithmetic-geometric mean ConvergenceOfASequenceWithFiniteUpcrossings convergence of a sequence with finite upcrossings ConvergenceOfComplexTermSeries convergence of complex term series ConvergenceOfIntegrals convergence of integrals ConvergenceOfRiemannZetaSeries convergence of Riemann zeta series