Primes. A prime number is not divisible by any number other than 1 and itself. Primes have many applications in computer software, from cryptography to hash tables.

To test for primes, a method can analyze a number for divisors. Some optimizations though are important: this speeds up prime detection. And caches are also helpful.

Isprime method. We begin with the isprime method. It receives a candidate integer. It returns True or False based on whether it can detect a factor—whether the number is prime.

First part The isprime method uses an if-statement, with a modulo division, to weed out even numbers. It special-cases 2 (a prime).

For, range This part loops, starting at 3, through all possible factors. It increments by 2, skipping evens.

Square In the for-loop, we eliminate a possible factor "i" if its square is more than the candidate number. This speeds things up.

Python program that checks for prime numbers

def isprime(candidate):
# No primes are even except 2.# ... Use modulo division to test for even numbers.
if (candidate % 2) == 0:
if candidate == 2:
return True
else:
return False
# Loop over numbers incrementing by 2 to the number.
for i in range(3, candidate, 2):
# No prime can be more than the square root.
if (i * i) > candidate:
break;
# See if the number is evenly divisible.
if (candidate % i) == 0:
return False
# The candidate is a prime unless it is 1.
return candidate != 1
# Test for primes in first 100 numbers.
for test in range(0, 100):
if isprime(test):
print(test)
# Test for primes in another range.
for test in range(10000, 10100):
if isprime(test):
print(test)
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97
10007
10009
10037
10039
10061
10067
10069
10079
10091
10093
10099

With modulo division, we test if a number is evenly divisible by another number. This is efficient. But other parts, like the for-loop, will be slow in extensive use.

Memoization. This is an approach to optimize repeated calculations. In memoization (which is not misspelled, referring to "memo") a method's result is stored in a dictionary.

Tip Memoization is a good optimization to apply to a method like isprime above.

Also Another option is to generate a list or dictionary of known primes and reuse it.

A brief history of primes. This prime-detecting method is a numerically intense one. With a JIT compiler, or a numeric optimization library for Python, performance improves.