A325902

Fifty is a peculiar integer.
When looking at its neighbors — the largest integer strictly beneath and the smallest strictly above –, more specifically their prime factorization, one finds

49=\underbrace{7^2<50<3\cdot 17}_{7+7+3=17}=51,

notably there exists a partition of the neighbor’s factors into two multisets such that both parts’ sums equal another.

Positive integers with the above described property can be found in my most recent addition to the OEIS: sequence A325902.

Factorization

Playing around with prime numbers, I created this simple factorization program.
The interesting thing about prime factors is that they are unique. There can only be one way to multiply prime numbers to get n where n \in \mathbb{N} and n \geq 2 (excluding the commutative property).
For example, 2 \cdot 3 \cdot 7 = 42 and that is the only way to multiply prime numbers to get to 42.
Factorizing some numbers...


# Python 2.7.7 Code
# Jonathan Frech 8th of April, 2016

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JClock VII

This alternative clock is not really readable by human. It calculates the first 144¹ primes, assigns 60 of them to every possible second, 60 to every possible minute and 24 to every possible hour.
Multiplying those three primes for a given time results in a composite number representing said time. Using integer factorization, you then can get the three primes back, map them to seconds, minutes and hours, and by doing so calculate the time.

2 minutes of prime time¹This number is the sum of 60 seconds, 60 minutes and 24 hours.


# Python 2.7.7 Code
# Pygame 1.9.1 (for Python 2.7.7)
# Jonathan Frech 13th of November, 2015

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