3 ms·

The main claim of the manuscript is essentially that primes correspond to the numbers whose residue modulo 2x3x5x7=210 is relatively prime to the modulus, i.e.,

The main claim of the manuscript is essentially that primes correspond to the numbers whose residue modulo 2x3x5x7=210 is relatively prime to the modulus, i.e., not divisible by 2, 3, 5, or 7. Two issues with this: (1) This is false. For example: every power of 211=2x3x5x7+1 is coprime with 210, and certainly every power of 211 above the first is not prime. (2) Even if one gives them credit and say they only claim a negative result, i.e., a number >7 that is not coprime to 210 is not prime, it is completely trivial. The manuscript does not contain any original idea of substance but does contain numerous false claims, the irresponsibility shown by various news sites in parroting this manuscript is astounding. This would never pass a peer review by any legitimate mathematician.

adrian_b 3y ago
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.

adrian_b 3y ago

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.