I am in need of finding prime numbers in arithmetic progression
80218110*n+8021749, n=1 to 100,000
I was told that using Sage would be a good option, since my computer is old. I happen to be new to Sage and I haven't found it to solve my problem, I guess it shouldn't be difficult, does anyone have a good reference for printing primes in arithmetic progressions?
SageMath is based on Python, and Python provides a syntax which should be comfortable for mathematicians:
[80218110*n + 8021749 for n in range(100)]
range(100) is the ordered set 0, 1, 2, ..., 99, and so the previous line evaluates 80218110*n + 8021749 for these values of n. We can also test whether the entries are prime:
INPUT: [80218110*n+8021749 for n in range(100) if (80218110*n+8021749).is_prime()]
OUTPUT:
[8021749,
489330409,
569548519,
970639069,
1050857179,
1131075289,
1772820169,
2093692609,
2173910719,
3136528039,
3617836699,
4660672129,
4740890239,
5382635119,
6425470549,
7067215429,
7227651649,
7548524089]
You can of course make the argument to range larger, but maybe it's not a good idea to print the whole list.
INPUT: len([80218110*n+8021749 for n in range(100000) if (80218110*n+8021749).is_prime()])
OUTPUT: 15273
(len returns the length of the list.) Producing this list is pretty quick, at least on my computer:
INPUT: %time L = [80218110*n+8021749 for n in range(100000) if (80218110*n+8021749).is_prime()]
OUTPUT CPU times: user 94.6 ms, sys: 1.13 ms, total: 95.8 ms
Wall time: 95.5 ms
(ms is milliseconds.)