[Daily puzzle] Prime number puzzle \ stacker news ~science

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[Daily puzzle] Prime number puzzle

615 sats \ 30 comments \ @south_korea_ln 26 Sep science

Find the largest known number that is the sum of two distinct primes in exactly two ways.

Hint: it's smaller than 100. If you find a bigger one, don't share it here.

The way I would tackle it is with a little Python script...

Posting a bit earlier than usual, won't have time later.

Previous iteration: #700785

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126 sats \ 0 replies \ @0xbitcoiner 26 Sep

37 + 31 = 61 + 7 = 68

216 sats \ 5 replies \ @SimpleStacker 26 Sep

I couldn't resist!

import pandas as pd
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]
data = []
for i in range(len(primes)):
    for j in range(i+1,len(primes)):
        x = primes[i]
        y = primes[j]
        z = x + y
        data.append({'z':z,'x':x,'y':y})
data = pd.DataFrame.from_dict(data)
counts = data.groupby('z').agg(count=('z','count'))
counts.loc[counts['count']==2]

The answer (conditional on being less than 100) is 68. But there are more that are greater than 100.

68 = 7 + 61 68 = 31 + 37

199 sats \ 2 replies \ @south_korea_ln OP 26 Sep

68 is correct.

Are you sure about the ones larger than 100 though? Maybe you need to add all the primes up to that supposed candidate number in your primes list to make sure they don't end up breaking that "exactly two" constraint.

123 sats \ 1 reply \ @SimpleStacker 26 Sep

Ah, you're right about larger than 100. I can't find one larger than 68. Revised script:

import pandas as pd

def get_primes(n):
    out = list()
    sieve = [True] * (n+1)
    for p in range(2, n+1):
        if (sieve[p]):
            out.append(p)
            for i in range(p, n+1, p):
                sieve[i] = False
    return out

n = 100
primes = get_primes(n)

data = []
for i in range(len(primes)):
    for j in range(i+1,len(primes)):
        x = primes[i]
        y = primes[j]
        z = x + y
        if z<=n:
            data.append({'z':z,'x':x,'y':y})
data = pd.DataFrame.from_dict(data)
counts = data.groupby('z').agg(count=('z','count')).reset_index()
counts.loc[counts['count']==2].sort_values(by='z',ascending=False).head(1)

I tried up to n=10,000 and nothing higher than 68 was found.

14 sats \ 0 replies \ @south_korea_ln OP 27 Sep

def get_primes(n): out = list() sieve = [True] * (n+1) for p in range(2, n+1): if (sieve[p]): out.append(p) for i in range(p, n+1, p): sieve[i] = False return out

Fancy pancy there with your Sieve of Eratosthenes ;)

0 sats \ 1 reply \ @zuspotirko 26 Sep

Smaller than 100 I wouldn't even have bothered with pandas lol. Good habit tho. The kind of script that I would have chatGPTed lol

0 sats \ 0 replies \ @SimpleStacker 26 Sep

I’m just so used to pandas that it’s the first method I thought of

21 sats \ 3 replies \ @WeAreAllSatoshi 26 Sep

Did you change territories on purpose?

121 sats \ 2 replies \ @south_korea_ln OP 26 Sep

I hadn't noticed. Force of habit i guess, ~science is where i usually post stuff except for these puzzles.

It'll be interesting to see how a well performing post affects my territory earnings though.

100 sats \ 1 reply \ @south_korea_ln OP 27 Sep

I'm tempted to keep posting them in ~science as this puzzle post seemed to have positively affected my territory fee earnings... not huge, but still, every little thing makes a difference in compensating the sats I'm losing at the moment.

It'll fit in the grand vision I have for this territory, where ~math will be one of the subterritories when that functionality rolls out...