Unsolved Problems due to Lack of Computational Power I was recently reading up about computational power and its uses in maths particularly to find counterexamples to conjectures. I was wondering are there any current mathematical problems which we are unable to solve due to our lack of computational power or inaccessibility to it.

What exactly am I looking for? 

Problems of which we know that they can be solved with a finite (but very long) computation? 

(e. g. NOT the Riemann hypothesis or twin prime conjecture)

I am looking for specific examples.
Goldbach's weak conjecture isn't a conjecture anymore, but before it was proved (in 2013), it had already been proved that it was true for every $n&gt;e^{e^{16\,038}}$. It was not computationally possible to test it for all numbers $n\leqslant e^{e^{16\,038}}$ though.
Prime gaps - https://en.wikipedia.org/wiki/Prime_gap - of maximum known merit are found by increasing CPU (and GPU) computational power on the gapcoin network. See: https://gapcoin.club


  ... So the difficulty will simply be the length of the prime gap?
  
  Not exactly. The average length of a prime gap with the starting prime
  p, is log(p), which means that the average prime gap size increases
  with lager primes. Then, instead of the pure length, we use the merit
  of the prime gap, which is the ratio of the gap's size to the average
  gap size.
  
  Let p be the prime starting a prime gap, then m = gapsize/log(p) will
  be the merit of this prime gap.
  
  Also a pseudo random number is calculated from p to provide finer
  difficulty adjustment.
  
  Let rand(p) be a pseudo random function with 0 less than rand(p) less
  than 1. Then, for a prime gap starting at prime p with size s, the
  difficulty will be s/log(p) + 2/log(p) * rand(p), where 2/log(p) is
  the average distance between a gap of size s and s + 2 (the next
  greater gap) in the proximity of p.
  
  When it actually comes to mining, there are two additional fields
  added to the Blockheader, named “shift” and “adder”. We will calculate
  the prime p as sha256(Blockheader) * 2^shift + adder. As an additional
  criterion the adder has to be smaller than 2^shift to avoid that the
  PoW could be reused. ...


Source: gapcoin.org

...

https://web.stanford.edu/~tonyfeng/bounded_gaps.pdf


  ... (Twin prime conjecture) ...
  
  ... This  is  a  just  a  special  case  of  a  far-reaching  conjecture 
  of  Hardy  and  Lit- tlewood  describing  the  frequency  of  prime 
  gaps  of  any  sizes.  The  Hardy- Littlewood conjecture predicts not
  only how often twin primes occur, but also how often any finite
  tuple of the form ( n
  + h 1 , n
  + h 2 , . . . , n
  + h k ) consists en- tirely of prime numbers. But even though analytic number theorists have be- lieved for many years that they know the
  answers to these questions, progress towards proving the existence of
  small gaps between primes has been slow. As recently as 2005 , the
  problem of establishing infinitely many bounded gaps be- tween primes
  was considered by many mathematicians to be “hopeless” ...


...

Further,

List of unsolved problems in mathematics:
https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics