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What does CLE stand for?

CLE stands for Cohen and Lenstra

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What about even larger N's? It is always possible to find the necessary factors. In fact it has been shown that there is always an integer m with m < (log n)log log log n for which the factors q dividing nm-1 with q-1 dividing m, have a product at least the size of the square root of n. Usually m is around 100,000,000 for numbers n with about 3,000 digits. This is roughly (very roughly!) how Adleman, Pomerance and Rumely began the modern age of primality testing by introducing the APR primality test [APR83] in 1979. The running time of their method is almost polynomial--its running time t is bounded as follows (log n)(c1 log log log n) < t < (log n)(c2 log log log n) (recognize those bounds?) Soon Cohen and Lenstra.