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"... We discuss a method for computing ∑ ..."
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|Venue:||Proceedings of the 7th International Symposium on Algorithmic Number Theory (ANTSVII|
... curves. 1. Introduction Following Lehmer in , given a real x ≥ 1, we say that a nonsquare positive integer n is an x-pseudosquare if n ≡ 1 (mod 8) and (n/p) = 1 for each odd prime p ≤ x, see also =-=[13, 15, 16, 17]-=- for further results. Here we generalise this notion and introduce and study x-pseudopoints on algebraic curves. More precisely, given an absolutely irreducible polynomial f(U, V ) ∈ Z[U, V ] and an i...
... in roughly cubic time, if a sufficiently large pseudosquare or pseudocube is available. In particular, the pseudosquares prime test is very useful in the context of finding all primes in an interval =-=-=-, where sieving can be used in place of trial division. This, then, motivates the search for larger and larger peudosquares and pseudocubes, and attempts to predict their distribution. See, for exampl...
...oach for large x, but it is useful for evaluating the accuracy of approximation algorithms, which is what we do here. So we wrote a program to do this, based on a segmented sieve of Eratosthenes (see =-=-=- for prime number sieve references), and we ran our program up to x = 1099511627776 = 240. Our results for this largest value for x appear in Table 1, which took just over 100 CPU hours to compute. AP...
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