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We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for extracting the periodicity of a function, and their combined use in the counting algorithm originally introduced by Brassard et al. One of the main features of our quantum probabilistic algorithm is its full unitarity and reversibility, which would make its use possible as part of larger and more complicated networks in quantum computers. As an example of this we describe polynomial time algorithms for studying some important problems in number theory, such as the test of the primality of an integer, the so called 'prime number theorem' and Hardy and Littlewood's conjecture about the asymptotic number of representations of an even integer as a sum of two primes.

We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for extracting the periodicity of a function, and their combined use in the counting algorithm originally introduced by Brassard et al. One of the main features of our quantum probabilistic algorithm is its full unitarity and reversibility, which would make its use possible as part of larger and more complicated networks in quantum computers. As an example of this we describe polynomial time algorithms for studying some important problems in number theory, such as the test of the primality of an integer, the so called 'prime number theorem' and Hardy and Littlewood's conjecture about the asymptotic number of representations of an even integer as a sum of two primes.

We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for extracting the periodicity of a function, and their combined use in the counting algorithm originally introduced by Brassard et al. One of the main features of our quantum probabilistic algorithm is its full unitarity and reversibility, which would make its use possible as part of larger and more complicated networks in quantum computers. As an example of this we describe polynomial time algorithms for studying some important problems in number theory, such as the test of the primality of an integer, the so called 'prime number theorem' and Hardy and Littlewood's conjecture about the asymptotic number of representations of an even integer as a sum of two primes.

We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for extracting the periodicity of a function, and their combined use in the counting algorithm originally introduced by Brassard et al. One of the main features of our quantum probabilistic algorithm is its full unitarity and reversibility, which would make its use possible as part of larger and more complicated networks in quantum computers. As an example of this we describe polynomial time algorithms for studying some important problems in number theory, such as the test of the primality of an integer, the so called 'prime number theorem' and Hardy and Littlewood's conjecture about the asymptotic number of representations of an even integer as a sum of two primes.

We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the distribution of an additive function on the integers, and its distribution on the primes.

LibriVox volunteers bring you 10 recordings of In these days . . . by Ebenezer Elliott. This was the Fortnightly Poetry project for May 23rd, 2010.

2Cookie 'n' Cracker Cookin'

By Jeanette Hindman Elliott and Alfred Festen

This is a short recipe book published by the United Biscuit Company of America, later to become the Keebler Company. Each recipe features one or more of their products the best known of which are Club Crackers, Town House Crackers, Honey Grahams, and Saltine Crackers. Categories range from appetizers through desserts. - Summary by Larry Wilson

Poems from the author of the beloved hymn, "Just as I Am", chiefly adapted to seasons of sickness, depression and bereavement. Elliott revised this collection of poems several times during her lifetime. This reading is from the 1836 edition. (Summary by MaryAnn)

4Planet of Shame

By Bruce Elliott

The Planet of Shame, by Bruce Elliott, is a semi-comical science fiction novel written in the early 1960s. Set in the quasi-distant future on a penal colony planet far enough away to be isolated, it relates the adventures and misadventures of James (Jimmy) Comstock and a small group of his associates who possess more heart than head, as they confront an anti-science and anti-intellectual power structure that has ossified and threatens to fall under its own weight. Many of the mores and norms of the earthbound home have been inverted, leading to a society that barely functions. “You don’t spit in the wind, you don’t pull the beard from the… - Summary by Bob Cherny