216 sats \ 5 replies \ @SimpleStacker 26 Sep \ on: [Daily puzzle] Prime number puzzle science
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
write
preview
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.
reply
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.
reply
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 ;)
reply
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
reply
0 sats \ 0 replies \ @SimpleStacker 26 Sep
I’m just so used to pandas that it’s the first method I thought of
reply