Goldbach & the primes
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A hub of small interactive pages exploring the Goldbach conjecture and the primes. Choose one to dive in.
essayThe block proofThe folded-strip attempt on Goldbach — holes, factors, and where it honestly stops.open →interactivePairingsSplit an even number into every pairing and knock out the composites.open →interactiveFirst primesFor every even number, its list of first primes. 100 → 3, 11, 17, 29, 41, 47.open →plotThe cometEvery even number vs its Goldbach-pair count — the famous banded comet.open →plotPrimesEvery prime as an Ulam spiral or grid, up to 10 million. Watch the diagonals.open →plotDifferencesPrime gaps, then the gaps between gaps, then between those — stacked bars.open →interactiveUnit-block sieveCarve the odds into primes, then rebuild the even number from two of them.open →interactiveBucketsPrimes as buckets poured in pairs to fill each even number exactly.open →interactiveBasesThe same Goldbach pairs written in base 2, 3, and 4 — identical truth.open →interactiveAlways roomSieve the window, watch the third of the space that always survives.open →findingThe N−1 = (k+1)p patternYour q = kp+1 idea, checked to a million — where it holds, and where it connects.open →findingPrime squares & last digitsWhy a prime squared usually has last two digits adding to a prime — and why it isn't about primes.open →findingLucky primes?Do 3, 5, 7 get luckier at making Goldbach pairs as N grows? Turns out it's a dead heat.open →findingWorst-case hunterAn equation (N = 2^k) for the even numbers most likely to break Goldbach — and the odds there.open →findingCovering systemsPick a remainder for 3, 5, 7, 9, 11 and try to catch every integer. The best you can do is 65.37% — and why is an open problem.open →plotRunning sumsSum of primes vs sum of non-primes up the number line. Primes lead through 7, then lose the lead forever.open →notesMy pathEverything tried this far — the conjectures, with honest verdicts.open →essayState of the attack~280 years of attempts on Goldbach, and where the frontier sits today.open →