  Let F be a random k-SAT formula on n variables, formed by selecting uniformly
and independently m = rn out of all possible k-clauses. It is well-known that
if r>2^k ln 2, then the formula F is unsatisfiable with probability that tends
to 1 as n tends to infinity. We prove that there exists a sequence t_k = O(k)
such that if r < 2^k ln 2 - t_k, then the formula F is satisfiable with
probability that tends to 1 as n tends to infinity.
  Our technique yields an explicit lower bound for the random k-SAT threshold
for every k. For k>3 this improves upon all previously known lower bounds. For
example, when k=10 our lower bound is 704.94 while the upper bound is 708.94.
