Block #366,392

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/19/2014, 9:22:04 AM · Difficulty 10.4293 · 6,441,642 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ab3c07cd7576fcd46b2ac97d94440d78290c99c384cc891225564ccc081e0409

View on Chainz ↗

Height

#366,392

Difficulty

10.429257

Transactions

Size

1.44 KB

Version

Bits

0a6de3cd

Nonce

11,950

Timestamp

1/19/2014, 9:22:04 AM

Confirmations

6,441,642

Mined by

⛏️ 8YAM4c6u8dYeQBkdo3RbtZ8WqY8DwUNSLEd4

Merkle Root

ca895a5f0f2dcac3c852f4281ee461177a05d42c63d99ea0bc8ad8c03dc6dce5

Transactions (4)

Coinbase9eb3520b538d89…e45534719b5d6b

1 in → 19 out9.2100 XPM709 B

AM4c6u8d…wUNSLEd4 AFutDVqJ…TJTJj6UF AczyTBWn…bEQQj33u AaJwNkvB…uqCwyjYa AcV6Mfwh…VmSjCD4e

d70bb3349b9db3…5ed0556561d338

1 in → 2 out6.0511 XPM226 B

AUPUoc5g…GgV3YmCs AW1RMRkS…7xhVZ4oc

12d0d65cd33155…f7c00b9c44f848

1 in → 2 out5.0001 XPM226 B

ANGzcdnj…8ntfuQ5C Ad4h6VGP…W7rTLKfo

6fa32972d9aa94…3924141694a48d

1 in → 2 out3.9868 XPM227 B

Ac24WwPt…BSeTbxUj AbEmsRcN…v1vFBckH

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.

5.014 × 10⁹²(93-digit number)

50143860020316418641…68624567763583151899

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

5.014 × 10⁹²(93-digit number)

50143860020316418641…68624567763583151899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.014 × 10⁹²(93-digit number)

50143860020316418641…68624567763583151901

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

1.002 × 10⁹³(94-digit number)

10028772004063283728…37249135527166303799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.002 × 10⁹³(94-digit number)

10028772004063283728…37249135527166303801

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

2.005 × 10⁹³(94-digit number)

20057544008126567456…74498271054332607599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.005 × 10⁹³(94-digit number)

20057544008126567456…74498271054332607601

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

4.011 × 10⁹³(94-digit number)

40115088016253134912…48996542108665215199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.011 × 10⁹³(94-digit number)

40115088016253134912…48996542108665215201

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

8.023 × 10⁹³(94-digit number)

80230176032506269825…97993084217330430399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.023 × 10⁹³(94-digit number)

80230176032506269825…97993084217330430401

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 #366,392

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