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 2017-05-20, 16:24 #265 sweety439     Nov 2016 8C816 Posts In this case, although (k*b^n+1)/gcd(k+1,b-1) has neither covering set nor algebra factors, but this form still cannot have a prime, thus this case is also excluded in the conjectures. (this situation only exists in the Sierpinski side) b = q^m, k = q^r, where q is not of the form t^s with odd s>1, and m and r have no common odd prime factor, and the exponent of highest power of 2 dividing r >= the exponent of highest power of 2 dividing m, and the equation 2^x = r (mod m) has no solution. Examples: b = q^7, k = q^r, where r = 3, 5, 6 (mod 7). b = q^14, k = q^r, where r = 6, 10, 12 (mod 14). b = q^15, k = q^r, where r = 7, 11, 13, 14 (mod 15). b = q^17, k = q^r, where r = 3, 5, 6, 7, 10, 11, 12, 14 (mod 17). b = q^21, k = q^r, where r = 5, 10, 13, 17, 19, 20 (mod 21) b = q^23, k = q^r, where r = 5, 7, 10, 11, 14, 15, 17, 19, 20, 21, 22 (mod 23) b = q^28, k = q^r, where r = 12, 20, 24 (mod 28) b = q^30, k = q^r, where r = 14, 22, 26, 28 (mod 30) b = q^31, k = q^r, where r = 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 (mod 31) b = q^33, k = q^r, where r = 5, 7, 10, 13, 14, 19, 20, 23, 26, 28 (mod 33) etc. (these are all examples for m<=33) Last fiddled with by sweety439 on 2017-06-09 at 00:27