Block #431,862

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 12:05:14 PM · Difficulty 10.3430 · 6,376,882 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f608b26aab65a55fe288dc302e70ac1a2409bc97eff2d553619fbd8f35cd0d5b

View on Chainz ↗

Height

#431,862

Difficulty

10.343030

Transactions

Size

1.67 KB

Version

Bits

0a57d0d4

Nonce

254,735

Timestamp

3/6/2014, 12:05:14 PM

Confirmations

6,376,882

Mined by

⛏️ aSdKAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

b77da1e1af3cc733503acddac5874a078d00ed05dbb5a9da06cb12f8905a828f

Transactions (2)

Coinbase1dcd46ef36a9a4…a8dca33a899bcf

1 in → 26 out9.3300 XPM947 B

Aac9Hjdg…P4ktypc3 AbC2pQ2N…LT6CeH7N AQBFkvAb…PV4vhdiA AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

c275784b5d5075…92a3c0ca5fab98

4 in → 2 out33.1717 XPM670 B

AbJ8RDhm…nTwXjj23 Adnmwr7c…BticWu6P

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.

1.903 × 10⁹⁵(96-digit number)

19036127437132556910…67677249398625414399

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

1.903 × 10⁹⁵(96-digit number)

19036127437132556910…67677249398625414399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.903 × 10⁹⁵(96-digit number)

19036127437132556910…67677249398625414401

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

3.807 × 10⁹⁵(96-digit number)

38072254874265113820…35354498797250828799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.807 × 10⁹⁵(96-digit number)

38072254874265113820…35354498797250828801

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

7.614 × 10⁹⁵(96-digit number)

76144509748530227641…70708997594501657599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.614 × 10⁹⁵(96-digit number)

76144509748530227641…70708997594501657601

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

1.522 × 10⁹⁶(97-digit number)

15228901949706045528…41417995189003315199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.522 × 10⁹⁶(97-digit number)

15228901949706045528…41417995189003315201

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

3.045 × 10⁹⁶(97-digit number)

30457803899412091056…82835990378006630399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.045 × 10⁹⁶(97-digit number)

30457803899412091056…82835990378006630401

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 #431,862

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