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An n-manifold which cannot be "nontrivially" decomposed into other n-manifolds.

Find the m×n array of single digits which contains the maximum possible number of primes, where allowable primes may lie along any horizontal, vertical, or diagonal line. For ...

Catalan (1876, 1891) noted that the sequence of Mersenne numbers 2^2-1=3, 2^3-1=7, and 2^7-1=127, and (OEIS A007013) were all prime (Dickson 2005, p. 22). Therefore, the ...

Let p_i denote the ith prime, and write m=product_(i)p_i^(v_i). Then the exponent vector is v(m)=(v_1,v_2,...).

The sequence of numbers obtained by letting a_1=2, and defining a_n=lpf(1+product_(k=1)^(n-1)a_k) where lpf(n) is the least prime factor. The first few terms are 2, 3, 7, 43, ...

A composite knot is a knot that is not a prime knot. Schubert (1949) showed that every knot can be uniquely decomposed (up to the order in which the decomposition is ...

The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

A pair of consecutive primes whose digits are rearrangements of each other, first considered by A. Edwards in Aug. 2001. The first few are (1913, 1931), (18379, 18397), ...

The cototient of a positive number n is defined as n-phi(n), where n is the totient function. It is therefore the number of positive integers <=n that have at least one prime ...

There are two sorts of transforms known as the fractional Fourier transform. The linear fractional Fourier transform is a discrete Fourier transform in which the exponent is ...