Block #476,744

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2014, 12:53:46 AM · Difficulty 10.4750 · 6,339,221 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b57e81b94f0592571121bc03d1d6bd32916ef6fda65b459ec44b7a6ab396bfdb

View on Chainz ↗

Height

#476,744

Difficulty

10.475024

Transactions

Size

651 B

Version

Bits

0a799b34

Nonce

1,203,848,780

Timestamp

4/6/2014, 12:53:46 AM

Confirmations

6,339,221

Mined by

⛏️ P2SHAJWou636Ah29w2HCH1NdEGponkUvn145Ad

Merkle Root

51306eb3c471d2eecf8f644b72b8c039b0cf13d4210b1c3430015c96587e7e2a

Transactions (3)

Coinbase2657a2136e63cb…365d9088367e64

1 in → 1 out9.1200 XPM109 B

AJWou636…Uvn145Ad

5975e92d166ce8…0f5e295f725542

1 in → 2 out5.3507 XPM227 B

AKK4XgkN…kppEHvvu AMCQE4Sg…Rhm4UXaY

a8269acf1cf7a2…7752f3dddf84d1

1 in → 2 out4.5003 XPM226 B

AG2xAdkr…SuMGaHDX ATrwP66U…xwKUWfay

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.

3.309 × 10⁹²(93-digit number)

33097116073594197739…06602098130178414679

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

3.309 × 10⁹²(93-digit number)

33097116073594197739…06602098130178414679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.309 × 10⁹²(93-digit number)

33097116073594197739…06602098130178414681

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

6.619 × 10⁹²(93-digit number)

66194232147188395479…13204196260356829359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.619 × 10⁹²(93-digit number)

66194232147188395479…13204196260356829361

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

1.323 × 10⁹³(94-digit number)

13238846429437679095…26408392520713658719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.323 × 10⁹³(94-digit number)

13238846429437679095…26408392520713658721

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

2.647 × 10⁹³(94-digit number)

26477692858875358191…52816785041427317439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.647 × 10⁹³(94-digit number)

26477692858875358191…52816785041427317441

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

5.295 × 10⁹³(94-digit number)

52955385717750716383…05633570082854634879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.295 × 10⁹³(94-digit number)

52955385717750716383…05633570082854634881

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 #476,744

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