Block #377,334

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2014, 1:06:21 AM · Difficulty 10.4233 · 6,449,656 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f739acc02bb4b4ee05f3d179528ea57e1ccd4815edb2b011036b4a4671f58567

View on Chainz ↗

Height

#377,334

Difficulty

10.423311

Transactions

Size

1.83 KB

Version

Bits

0a6c5e20

Nonce

74,882

Timestamp

1/27/2014, 1:06:21 AM

Confirmations

6,449,656

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ca7902916260c7da66d4797bf63f9a726835028c4095db8bbefddaa31fa162fa

Transactions (2)

Coinbase9f3273a024da19…cfc6bd14ef32d2

1 in → 26 out9.1900 XPM947 B

AQvZBsUo…hppgRZTJ AFutDVqJ…TJTJj6UF Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6

61a557728bf885…3518a265ab11ad

4 in → 10 out31.4286 XPM840 B

Ad4XAfRG…ePHYewUC AQXHoyAf…Ug76XPmT AZfJBbCQ…7AystqGz AVpkHmLi…W2eTY6gd AYjQEpde…m1JSNW9c

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.

1.434 × 10⁹⁴(95-digit number)

14343006000032299237…41546404617515239679

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

1.434 × 10⁹⁴(95-digit number)

14343006000032299237…41546404617515239679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.434 × 10⁹⁴(95-digit number)

14343006000032299237…41546404617515239681

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

2.868 × 10⁹⁴(95-digit number)

28686012000064598475…83092809235030479359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.868 × 10⁹⁴(95-digit number)

28686012000064598475…83092809235030479361

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

5.737 × 10⁹⁴(95-digit number)

57372024000129196950…66185618470060958719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.737 × 10⁹⁴(95-digit number)

57372024000129196950…66185618470060958721

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

1.147 × 10⁹⁵(96-digit number)

11474404800025839390…32371236940121917439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.147 × 10⁹⁵(96-digit number)

11474404800025839390…32371236940121917441

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

2.294 × 10⁹⁵(96-digit number)

22948809600051678780…64742473880243834879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.294 × 10⁹⁵(96-digit number)

22948809600051678780…64742473880243834881

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 #377,334

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