Primes, Alpha Code

primes-to-alpha.md

https://oeis.org/A000040

Primes mapped to alpha values.

a 2
b 3
c 5
d 7
e 11
f 13
g 17
h 19
i 23
j 29
k 31
l 37
m 41
n 43
o 47
p 53
q 59
r 61
s 67
t 71
u 73
v 79
w 83
x 89
y 97
z 101

In 5th grade, we had to use primes to make a product that would represent a word. To decode a number to a word you had to do the prime factorization.

Everyone had calculators that could represent 8 digits.

We had fun doing prime factorization with words that day. I frustrated some classmates by giving them the coded words:

math is power

Power comes out to 138731263, which did not fit on anyone's calculator. :)

So for a 5th grader to solve it you had to be a bit smarter if you didn't want to take all day.

You would try the vowels first or other common english letters first before just all the primes in order.

Dividing by 11, would get you a number that would fit on the calculator screen.

primes-to-alpha.py

primes = [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, 101]
alpha = 'abcdefghijklmnopqrstuvwxyz'

for p,a in zip(primes, alpha):
    print(a, p)

p2a = { p:a for p,a in zip(primes, alpha)}
a2p = { a:p for p,a in zip(primes, alpha)}
def word_to_num(word):
    prod = 1
    for a in word:
        prod *= a2p[a]
    return prod

word_to_num('power')
# 138731263
word_to_num('math')
# 110618
word_to_num('is')
# 1541
138731263/11
# 12611933.0
p2a[11]
# 'e'
def num_to_word(num):
    # try dividing by each prime
    # if it is divisible, add it to the list of prime factorizations
    primes = []
    for p in p2a.keys():
       if num%p == 0:
           primes.append(p)
    for p in primes:
       print(p2a[p], end='')

num_to_word(138731263)