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Let p be an odd prime, k be an integer such that pk and 1<=k<=2(p+1), and N=2kp+1. Then the following are equivalent 1. N is prime. 2. There exists an a such that ...

The positive real axis is the portion of the real axis with x>0.

The complex plane C with the origin removed, i.e., C-{0}. The punctured plane is sometimes denoted C^* (although this notation conflicts with that for the Riemann sphere C-*, ...

The positive rational numbers, denoted Q^+.

"The reals" is a common way of referring to the set of real numbers and is commonly denoted R.

The portion of the complex plane z=x+iy with real part R[z]>0.

One of a set of numbers defined in terms of an invariant generated by the finite cyclic covering spaces of a knot complement. The torsion numbers for knots up to 9 crossings ...

An infinite set, such as the real numbers, which is not countably infinite.

The unit upper half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]>0}.

A modification of the Eberhart's conjecture proposed by Wagstaff (1983) which proposes that if q_n is the nth prime such that M_(q_n) is a Mersenne prime, then ...