Block #381,514

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/30/2014, 1:33:27 AM · Difficulty 10.4047 · 6,426,354 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b4061642b5b654dd3d649df1c754c1f9e1b37b45315c5a341079ed3a56945f86

View on Chainz ↗

Height

#381,514

Difficulty

10.404748

Transactions

Size

427 B

Version

Bits

0a679d8c

Nonce

15,034

Timestamp

1/30/2014, 1:33:27 AM

Confirmations

6,426,354

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

08a2b8b1d139a62dfa3e40a3898e72cb31ab4a7b5ddce0c16cda319f53d97dd1

Transactions (2)

Coinbasede308436a6cda5…484cc022560e36

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

820eaa3f593ece…5d133e0750eb4b

1 in → 2 out2.0367 XPM225 B

AHcuE8zL…RMdrKcps Ab2py7Wd…ASeTzoAv

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.

8.033 × 10⁹⁸(99-digit number)

80330997318948424699…63548282610264355839

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

8.033 × 10⁹⁸(99-digit number)

80330997318948424699…63548282610264355839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.033 × 10⁹⁸(99-digit number)

80330997318948424699…63548282610264355841

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

1.606 × 10⁹⁹(100-digit number)

16066199463789684939…27096565220528711679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.606 × 10⁹⁹(100-digit number)

16066199463789684939…27096565220528711681

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

3.213 × 10⁹⁹(100-digit number)

32132398927579369879…54193130441057423359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.213 × 10⁹⁹(100-digit number)

32132398927579369879…54193130441057423361

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

6.426 × 10⁹⁹(100-digit number)

64264797855158739759…08386260882114846719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.426 × 10⁹⁹(100-digit number)

64264797855158739759…08386260882114846721

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

1.285 × 10¹⁰⁰(101-digit number)

12852959571031747951…16772521764229693439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.285 × 10¹⁰⁰(101-digit number)

12852959571031747951…16772521764229693441

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 #381,514

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