project_euler.problem_077.sol1¶

It is possible to write ten as the sum of primes in exactly five different ways:

7 + 3 5 + 5 5 + 3 + 2 3 + 3 + 2 + 2 2 + 2 + 2 + 2 + 2

What is the first value which can be written as the sum of primes in over five thousand different ways?

Attributes¶

`partition`(→ set[int])	Return a set of integers corresponding to unique prime partitions of n.
`solution`(→ int \| None)	Return the smallest integer that can be written as the sum of primes in over

project_euler.problem_077.sol1.partition(number_to_partition: int) → set[int]¶: Return a set of integers corresponding to unique prime partitions of n. The unique prime partitions can be represented as unique prime decompositions, e.g. (7+3) <-> 7*3 = 12, (3+3+2+2) = 3*3*2*2 = 36 >>> partition(10) {32, 36, 21, 25, 30} >>> partition(15) {192, 160, 105, 44, 112, 243, 180, 150, 216, 26, 125, 126} >>> len(partition(20)) 26

project_euler.problem_077.sol1.solution(number_unique_partitions: int = 5000) → int | None¶: Return the smallest integer that can be written as the sum of primes in over m unique ways. >>> solution(4) 10 >>> solution(500) 45 >>> solution(1000) 53