Python Prime Number Method

Check to see if a value is a prime number, introducing an isprime method.

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.Numbers

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) Output 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.For

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.MemoizeDictionary

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.
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