Category talk:Wren-math: Difference between revisions
→Source code: Added squareFree, cubeFree and powerFree methods to Int class.
(→Source code: Added Int.primePowers method.) |
(→Source code: Added squareFree, cubeFree and powerFree methods to Int class.) |
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Line 485:
n = n - 2
}
}
// Returns the 'n'th prime number. For the formula used, see:
// https://en.wikipedia.org/wiki/Prime_number_theorem#Approximations_for_the_nth_prime_number
static getPrime(n) {
if (n < 1 || !n.isInteger) Fiber.abort("Argument must be a positive integer.")
if (n < 8) return [2, 3, 5, 7, 11, 13, 17][n-1]
var l1 = n.log
var l2 = l1.log
var l3 = (l2 - 2) / l1
var l4 = (l2*l2 - 6*l2 + 11) / (2*l1*l1)
var p = ((l1 + l2 + l3 - l4 - 1) * n).floor
var g = p.log.round
var pc = Int.primeCount(p)
p = p + (n - pc) * g
if (p % 2 == 0) p = p - 1
pc = Int.primeCount(p)
if (pc < n) {
for (i in pc...n) p = Int.nextPrime(p)
} else if (Int.isPrime(p)) {
for (i in n...pc) p = Int.prevPrime(p)
} else {
for (i in n..pc) p = Int.prevPrime(p)
}
return p
}
Line 735 ⟶ 760:
return res
}
// Returns true if the prime factorization of 'n' does not contain any
// factors which are repeated 'm' (or more) times, or false otherwise.
static powerFree(m, n) { Int.primePowers(n).all { |pp| pp[1] < m } }
// Covenience versions of above method for squares and cubes.
static squareFree(n) { powerFree(2, n) }
static cubeFree(n) { powerFree(3, n) }
// Returns all the divisors of 'n' including 1 and 'n' itself.
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