Block #341,837

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/3/2014, 5:08:12 PM · Difficulty 10.1448 · 6,464,175 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

75a962e50961a8045ce362501947f58b4559b50121cc80d8c4b72789b8155b33

View on Chainz ↗

Height

#341,837

Difficulty

10.144836

Transactions

Size

1.01 KB

Version

Bits

0a2513f6

Nonce

62,849

Timestamp

1/3/2014, 5:08:12 PM

Confirmations

6,464,175

Mined by

⛏️ M7aR{AQ8QAT3JKsV1xD6zC94z9djnpJrCFKuVbR

Merkle Root

fad9e98dd81cb8ff2d99d76dc475bedcb143d00133dc4dd79a16b42374cc13c8

Transactions (1)

Coinbasefad9e98dd81cb8…16b42374cc13c8

1 in → 26 out9.7000 XPM947 B

AQ8QAT3J…rCFKuVbR AYtDvcGs…VuAcA7m7 AG5YAjec…VhA4Aeh1 AQwRN8bE…V8PsTcY9 AFutDVqJ…TJTJj6UF

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.

3.916 × 10⁹⁷(98-digit number)

39169345491687281365…86565209145927029759

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

3.916 × 10⁹⁷(98-digit number)

39169345491687281365…86565209145927029759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.916 × 10⁹⁷(98-digit number)

39169345491687281365…86565209145927029761

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

7.833 × 10⁹⁷(98-digit number)

78338690983374562730…73130418291854059519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.833 × 10⁹⁷(98-digit number)

78338690983374562730…73130418291854059521

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

1.566 × 10⁹⁸(99-digit number)

15667738196674912546…46260836583708119039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.566 × 10⁹⁸(99-digit number)

15667738196674912546…46260836583708119041

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

3.133 × 10⁹⁸(99-digit number)

31335476393349825092…92521673167416238079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.133 × 10⁹⁸(99-digit number)

31335476393349825092…92521673167416238081

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

6.267 × 10⁹⁸(99-digit number)

62670952786699650184…85043346334832476159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.267 × 10⁹⁸(99-digit number)

62670952786699650184…85043346334832476161

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