Block #1,432,612

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2016, 10:04:36 AM · Difficulty 10.7879 · 5,385,292 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

6719a316b3cc4d11a1bf56bd40b2e9cd0f224c2fd122ab2856d0411bed59a0cd

View on Chainz ↗

Height

#1,432,612

Difficulty

10.787913

Transactions

Size

1.64 KB

Version

Bits

0ac9b4af

Nonce

447,173,720

Timestamp

1/28/2016, 10:04:36 AM

Confirmations

5,385,292

Mined by

⛏️ P2SHAFmz6afzwgopR37XHKkQn3p1hvRN8nZjF3

Merkle Root

d05786fddb952e9fe2603de42d728e76f52584dbec3a4f2d213f6ca7add9f5b0

Transactions (3)

Coinbase7fb33182f348f9…dca6989d3e451e

1 in → 1 out8.6000 XPM110 B

AFmz6afz…RN8nZjF3

caa2a51d01f34e…86926c7977c6a6

5 in → 2 out584.8000 XPM915 B

AV7kZd6h…No16W2ox ANDHgH3W…JfsCGx7T

b89dfa263c3a2e…251ca760b6563f

1 in → 12 out173.3420 XPM567 B

Ac2aFd5d…aMXhNyZn AQrWCE7s…3Lg58QvA AG4pcGkr…GSEd3BvS AawB1NhV…oYZTQfdb AGskjDpg…pYnEzeYR

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.983 × 10⁹⁵(96-digit number)

29835236283825515340…64869224279040817919

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.983 × 10⁹⁵(96-digit number)

29835236283825515340…64869224279040817919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.983 × 10⁹⁵(96-digit number)

29835236283825515340…64869224279040817921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.967 × 10⁹⁵(96-digit number)

59670472567651030680…29738448558081635839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.967 × 10⁹⁵(96-digit number)

59670472567651030680…29738448558081635841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.193 × 10⁹⁶(97-digit number)

11934094513530206136…59476897116163271679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.193 × 10⁹⁶(97-digit number)

11934094513530206136…59476897116163271681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.386 × 10⁹⁶(97-digit number)

23868189027060412272…18953794232326543359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.386 × 10⁹⁶(97-digit number)

23868189027060412272…18953794232326543361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.773 × 10⁹⁶(97-digit number)

47736378054120824544…37907588464653086719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.773 × 10⁹⁶(97-digit number)

47736378054120824544…37907588464653086721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #1,432,612

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