Riesel case: (k*b^n1)/gcd(k1,b1)
Sierpinski case: (k*b^n+1)/gcd(k+1,b1)
If k is not rational power of b, then:
* In Riesel case, (k*b^n1)/gcd(k1,b1) has algebra factors if and only if k*b^n is perfect power (of the form m^r with r>1)
* In Sierpinski case, (k*b^n+1)/gcd(k+1,b1) has algebra factors if and only if k*b^n is either perfect odd power (of the form m^r with odd r>1) or of the form 4*m^4
If k is rational power of b (let k = m^r, b = m^s):
* In Riesel case, (k*b^n1)/gcd(k1,b1) has algebra factors if and only if n*s+r is composite
* In Sierpinski case, (k*b^n+1)/gcd(k+1,b1) has algebra factors if and only if n*s+r is (not power of 2, if valuation(r,2) >= valuation(s,2)) (not of the form p*2^valuation(r,2) with p prime, if valuation(r,2) < valuation(s,2))
Last fiddled with by sweety439 on 20200923 at 19:56
