TIL about prime-generating quadratic polynomials, as well. I feel like I’m destined to use one in code now. The logic behind eπ√163 looks like more than I can absorb today, haha.
Because I find Wikipedia doesn’t explain it in the best way, a quadratic field like ℚ[√-n] is literally just the field of rationals with √-n and all the new numbers you can make with it added.
The Heegner Numbers. These are the n such that ℚ[√-n] has unique factorisation. There are exactly 9 of them:
A famous fact about them is that 163 being a Heegner Number leads to e^(π√163) being very close to a whole number.
TIL about prime-generating quadratic polynomials, as well. I feel like I’m destined to use one in code now. The logic behind eπ√163 looks like more than I can absorb today, haha.
Because I find Wikipedia doesn’t explain it in the best way, a quadratic field like ℚ[√-n] is literally just the field of rationals with √-n and all the new numbers you can make with it added.