Block #323,561

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/21/2013, 5:39:30 PM · Difficulty 10.2064 · 6,501,807 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

78c2b3f7320b30bc9011de7d725b5561cdadba991087b0c893ea009cfc44db3e

View on Chainz ↗

Height

#323,561

Difficulty

10.206424

Transactions

Size

1.45 KB

Version

Bits

0a34d832

Nonce

5,320

Timestamp

12/21/2013, 5:39:30 PM

Confirmations

6,501,807

Mined by

⛏️ aR5tAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

f31f3393a96b8bf88ca3101efc23a356b2a70c262334c55dccdd4cd09ddbbb55

Transactions (2)

Coinbase91a85cd53c8f8a…71b0152ab3abce

1 in → 25 out9.5800 XPM913 B

Ad9pSzHt…cpJ3y2zz AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 AdCzCa8u…aUQkKZ8z AZ2pPuKg…95SN2Yr7

ce360f915eb066…ad90d8b6b43d5f

2 in → 7 out19.3600 XPM476 B

AWn9rWeZ…sxk6DT9k AV5DKmQ7…saMvPYKs AKXDwiQX…ByKkCqrj AGPVcumJ…jTfDP3FJ AebFVhKP…WJpqjZCK

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.

2.334 × 10⁹⁹(100-digit number)

23343125155224979977…59769027594934279359

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

2.334 × 10⁹⁹(100-digit number)

23343125155224979977…59769027594934279359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.334 × 10⁹⁹(100-digit number)

23343125155224979977…59769027594934279361

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

4.668 × 10⁹⁹(100-digit number)

46686250310449959954…19538055189868558719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.668 × 10⁹⁹(100-digit number)

46686250310449959954…19538055189868558721

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

9.337 × 10⁹⁹(100-digit number)

93372500620899919909…39076110379737117439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.337 × 10⁹⁹(100-digit number)

93372500620899919909…39076110379737117441

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

1.867 × 10¹⁰⁰(101-digit number)

18674500124179983981…78152220759474234879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.867 × 10¹⁰⁰(101-digit number)

18674500124179983981…78152220759474234881

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

3.734 × 10¹⁰⁰(101-digit number)

37349000248359967963…56304441518948469759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.734 × 10¹⁰⁰(101-digit number)

37349000248359967963…56304441518948469761

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 #323,561

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