Block #274,089

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 3:35:28 AM · Difficulty 9.9563 · 6,534,092 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fa41c6c876dc74b774a652e1c0d91dfc75babdf89958c633071b21cfdc6b6c14

View on Chainz ↗

Height

#274,089

Difficulty

9.956323

Transactions

Size

1.18 KB

Version

Bits

09f4d192

Nonce

192,592

Timestamp

11/26/2013, 3:35:28 AM

Confirmations

6,534,092

Mined by

⛏️ .aRlAWZd1qVJsLEYJ7QkpZDB3cXqFz9pj9yfPa

Merkle Root

4715a2decc022d22330322188a3e65f1630a9a67ce09900e7bf6522487f89f73

Transactions (1)

Coinbase4715a2decc022d…f6522487f89f73

1 in → 31 out10.0500 XPM1.09 KB

AWZd1qVJ…9pj9yfPa Abv8pzf1…t4zPXDTV AMbCuLHZ…WSoStwkc ANo4YY1x…vnsPRDSU AWrpzrQN…Axvr5NSY

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.

7.057 × 10⁹¹(92-digit number)

70578696114182916784…11676750037772462439

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

7.057 × 10⁹¹(92-digit number)

70578696114182916784…11676750037772462439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.057 × 10⁹¹(92-digit number)

70578696114182916784…11676750037772462441

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

1.411 × 10⁹²(93-digit number)

14115739222836583356…23353500075544924879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.411 × 10⁹²(93-digit number)

14115739222836583356…23353500075544924881

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

2.823 × 10⁹²(93-digit number)

28231478445673166713…46707000151089849759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.823 × 10⁹²(93-digit number)

28231478445673166713…46707000151089849761

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

5.646 × 10⁹²(93-digit number)

56462956891346333427…93414000302179699519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.646 × 10⁹²(93-digit number)

56462956891346333427…93414000302179699521

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

1.129 × 10⁹³(94-digit number)

11292591378269266685…86828000604359399039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #274,089

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