While I agree that there are great chances that their proofs contain some mistakes, what you say is completely erroneous. Their primality test is considerably

While I agree that there are great chances that their proofs contain some mistakes, what you say is completely erroneous. Their primality test is considerably more complex than what you say. Those numbers with coprime residues are just candidates for being primes and there are additional conditions that become more complex to compute for larger and larger numbers. There is absolutely no implication from what they say that a power of 211 could be prime. Their theorem: "An integer a in [11,b] containing no factors of 2, 3, 5, and 7 is a prime if and only if there exists r_i coprime with 210 and a non-negative integer k so that a = r_i + 210 × k with k+1 not in L_b[i]" "i" is in [1,48] and it is an index into an array with the 48 numbers coprime with 210 in the interval [11,211]. "L_b" is a table that must be computed from b with an algorithm given in the paper. I have not analyzed their proofs, so they may be wrong, or perhaps the computation of the L_b table is not actually faster than the sieving methods currently used, but everything written by you is not applicable to the paper.