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Exercise 4.5.48 (Same questions for even values)
Carry out the same process as in the preceding exercise for all even number less that . Explain the relative lengths of the lists versus the number of integers tested.
Answers
We complete the preceding program with the even values of :
max = 1000
l = [n for n in range(2,max) if n % 2 == 0 and not Integer(n).is_prime_power()
and not excluded(Integer(n))]; len(l)
490
for n in l:
n = Integer(n)
print ’n =’, n,’=’, factor(n)
for p, lp in sylow(n):
print ’ ’,p, ’=>’, lp
print
WARNING: Output truncated!
n = 6 = 2 * 3
2 => [1, 3]
3 => [1]
n = 10 = 2 * 5
2 => [1, 5]
5 => [1]
n = 12 = 2^2 * 3
2 => [1, 3]
3 => [1, 4]
n = 14 = 2 * 7
2 => [1, 7]
7 => [1]
n = 18 = 2 * 3^2
2 => [1, 3, 9]
3 => [1]
n = 20 = 2^2 * 5
2 => [1, 5]
5 => [1]
n = 22 = 2 * 11
2 => [1, 11]
11 => [1]
n = 24 = 2^3 * 3
2 => [1, 3]
3 => [1, 4]
n = 26 = 2 * 13
2 => [1, 13]
13 => [1]
n = 28 = 2^2 * 7
2 => [1, 7]
7 => [1]
...
n = 988 = 2^2 * 13 * 19
2 => [1, 13, 19, 247]
13 => [1]
19 => [1]
n = 990 = 2 * 3^2 * 5 * 11
2 => [1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, 495]
3 => [1, 10, 22, 55]
5 => [1, 6, 11, 66]
11 => [1, 45]
n = 992 = 2^5 * 31
2 => [1, 31]
31 => [1, 32]
n = 994 = 2 * 7 * 71
2 => [1, 7, 71, 497]
7 => [1, 71]
71 => [1]
n = 996 = 2^2 * 3 * 83
2 => [1, 3, 83, 249]
3 => [1, 4, 166]
83 => [1]
n = 998 = 2 * 499
2 => [1, 499]
499 => [1]
full_output.txt
Every number of the form with odd appears in this list. The only excluded values are the 8 powers of : .
