Specific discrete logarithm question I came across a DL that I need to solve... 

5^k = 6361196924231058595008858273263807320 (mod 15860584089531798358308118294328202587) 


The modulus is a 124 bit number, so generic Baby Step - Giant Step would take some $2^{62}$ operations, which is unfeasible on a home PC.

Is there any weakness to it? The modulus is 2 * another huge prime + 1, so definitely not smooth (and susceptible to Pohlig - Hellman). 

Apparently, some people solved it on their home PCs in a matter of hours... how? It seems impossible to me.
(12:15) gp &gt; p=15860584089531798358308118294328202587;
(12:15) gp &gt; y=6361196924231058595008858273263807320;
(12:15) gp &gt; x=znlog(Mod(y,p),Mod(5,p))
11473769387225613271575199155876761324
(12:17) gp &gt; ##
  ***   last result computed in 1min, 26,253 ms.
(12:17) gp &gt; Mod(5,p)^x == Mod(y,p)
1
(12:17) gp &gt;
firas@wakaba ~ % cat /proc/cpuinfo |grep 'model name'
model name      : Intel(R) Core(TM) i5-3330 CPU @ 3.00GHz


From the documentation:


  This function uses
  
  
  a combination of generic discrete log algorithms (see below).
  in $(\mathbb Z/N\mathbb Z)^*$ when $N$ is prime: a linear sieve index calculus method, suitable for $N &lt; 10^{50}$, say, is used for large prime divisors of the order.
  
  
  The generic discrete log algorithms are:
  
  
  Pohlig-Hellman algorithm, to reduce to groups of prime order $q$, where $q \mid p-1$ and $p$ is an odd prime divisor of $N$,
  Shanks baby-step/giant-step ($q &lt; 2^{32}$ is small),
  Pollard rho method ($q &gt; 2^{32}$).