Block #331,607

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2013, 11:53:02 AM · Difficulty 10.1681 · 6,485,171 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ccbc25effeeb5cfad97ccecd21c041e39c7fd30bb1af59bbb483cbc37ef6164

View on Chainz ↗

Height

#331,607

Difficulty

10.168115

Transactions

Size

2.14 KB

Version

Bits

0a2b0991

Nonce

21,282

Timestamp

12/27/2013, 11:53:02 AM

Confirmations

6,485,171

Mined by

⛏️ WaRjAFutDVqJywBDvDDzwUNgUinUiETJTJj6UF

Merkle Root

e5de64c65ab5ef1aa7f4f77d67ec6c138e24230ce92466ef3c470f034efb74a1

Transactions (4)

Coinbasefb3b60efb94a80…bd0c704b774f64

1 in → 27 out9.6600 XPM981 B

AFutDVqJ…TJTJj6UF Aac9Hjdg…P4ktypc3 AG5YAjec…VhA4Aeh1 AQ8QAT3J…rCFKuVbR AZ2pPuKg…95SN2Yr7

e61dd6b66fd19f…f4146916dca30d

3 in → 2 out25.7537 XPM524 B

AdEXaN4v…gTtGYj6K AHF7sQhG…bYN9ND34

4553b556f324b8…2057b6d7f799ab

2 in → 2 out17.2239 XPM373 B

AU1fG3ZU…VavhwYTd APBswfDk…4HU6j7iV

5591c6f2550903…f7514204891dbb

1 in → 2 out7.5896 XPM226 B

AasiSJ97…tPWLPQC9 AMBaesuK…6AGZoQG4

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.

5.476 × 10⁹⁵(96-digit number)

54768013364471252103…81122125654815884799

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

5.476 × 10⁹⁵(96-digit number)

54768013364471252103…81122125654815884799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.476 × 10⁹⁵(96-digit number)

54768013364471252103…81122125654815884801

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

1.095 × 10⁹⁶(97-digit number)

10953602672894250420…62244251309631769599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.095 × 10⁹⁶(97-digit number)

10953602672894250420…62244251309631769601

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

2.190 × 10⁹⁶(97-digit number)

21907205345788500841…24488502619263539199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.190 × 10⁹⁶(97-digit number)

21907205345788500841…24488502619263539201

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

4.381 × 10⁹⁶(97-digit number)

43814410691577001682…48977005238527078399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.381 × 10⁹⁶(97-digit number)

43814410691577001682…48977005238527078401

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

8.762 × 10⁹⁶(97-digit number)

87628821383154003365…97954010477054156799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.762 × 10⁹⁶(97-digit number)

87628821383154003365…97954010477054156801

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 #331,607

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