---
# System prepended metadata

title: Crypto/primimity

---

# Crypto/primimity
> People claim that RSA with two 1024-bit primes is secure. But I trust no one. That's why I use three 1024-bit primes.
I even created my own prime generator to be extra cautious!

Provided files: `primimity-public-key.txt` and `primimity.py`.

`primimity-public-key.txt`
```
n: 2739699434633097765008468371124644741923408864896396205946954196101304653772173210372608955799251139999322976228678445908704975780068946332615022064030241384638601426716056067126300711933438732265846838735860353259574129074615298010047322960704972157930663061480726566962254887144927753449042590678730779046154516549667611603792754880414526688217305247008627664864637891883902537649625488225238118503996674292057904635593729208703096877231276911845233833770015093213639131244386867600956112884383105437861665666273910566732634878464610789895607273567372933766243229798663389032807187003756226177111720510187664096691560511459141773632683383938152396711991246874813205614169161561906148974478519987935950318569760474249427787310865749167740917232799538099494710964837536211535351200520324575676987080484141561336505103872809932354748531675934527453231255132361489570816639925234935907741385330442961877410196615649696508210921
e: 65537
c: 2082926013138674164997791605512226759362824531322433048281306983526001801581956788909408046338065370689701410862433705395338736589120086871506362760060657440410056869674907314204346790554619655855805666327905912762300412323371126871463045993946331927129882715778396764969311565407104426500284824495461252591576672989633930916837016411523983491364869137945678029616541477271287052575817523864089061675401543733151180624855361245733039022140321494471318934716652758163593956711915212195328671373739342124211743835858897895276513396783328942978903764790088495033176253777832808572717335076829539988337505582696026111326821783912902713222712310343791755341823415393931813610365987465739339849380173805882522026704474308541271732478035913770922189429089852921985416202844838873352090355685075965831663443962706473737852392107876993485163981653038588544562512597409585410384189546449890975409183661424334789750460016306977673969147
```

`primimity.py`
```python
#!/usr/bin/env python3

from Crypto.Util.number import getRandomNBitInteger, isPrime

def find_next_prime(n):
    if n <= 1:
        return 2
    elif n == 2:
        return 3
    else:
        if n % 2 == 0:
            n += 1
        else:
            n += 2
        while not isPrime(n):
            n += 2
        return n
    
def prime_gen():
    i = getRandomNBitInteger(1024)
    d = getRandomNBitInteger(8)
    for _ in range(d):
        i = find_next_prime(i)
    p = find_next_prime(i)
    d = getRandomNBitInteger(8)
    for _ in range(d):
        i = find_next_prime(i)
    q = find_next_prime(i)
    d = getRandomNBitInteger(8)
    for _ in range(d):
        i = find_next_prime(i)
    r = find_next_prime(i)
    return (p,q,r)

def main():
    (p,q,r) = prime_gen()
    print(p)
    print(q)
    print(r)

if __name__ == '__main__':
    main()
```

There is a vulnerability in how the prime numbers are found. The first one is a random prime, the ones after that are the second next prime every time.
Probably, we need to find a prime close to log(n,3) I think.