Weaknesses in vanity PGP keys The program Scallion can generate vanity PGP keys and .onion addresses using the following method:


  
  Generate RSA key using OpenSSL on the CPU
  Send the key to the GPU
  Increase the key's public exponent
  Hash the key
  If the hashed key is not a partial collision go to step 3
  If the key does not pass the sanity checks recommended by PKCS #1 v2.1 (checked on the CPU) go to step 3
  Brand new key with partial collision!
  


As RSA is susceptible to various attacks when its parameters are not properly selected, e.g. small difference of prime factors, does this method of iteratively increasing the public exponent yield any weaknesses in the generated keys?

Of course, it is possible to generate a key with a fingerprint you desire using gpg itself but it is much slower.
This method is fine (if it does actually check for short private exponents).

Any choice of public exponent is functionally and security-wise equivalent as long as it doesn't induce a short private exponent and as long as it is co-prime to $\lambda(n)$. The latter being caught by the fact that key generation won't be able to finish and the former being caught by the PKCS#1 v2.1 induced check (which I couldn't actually find, so beware!), which should check for short private exponents.