Block #232,795

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/29/2013, 8:32:04 AM · Difficulty 9.9415 · 6,576,918 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9bec2b75a748119ed0d91eda0bef566dd8f2cc7c65d2459ba621d089d3717442

View on Chainz ↗

Height

#232,795

Difficulty

9.941478

Transactions

Size

1.97 KB

Version

Bits

09f104b3

Nonce

38,781

Timestamp

10/29/2013, 8:32:04 AM

Confirmations

6,576,918

Mined by

⛏️ RopAMypZdXSN9SRf28auDeE3guPFj5jJKu8wP

Merkle Root

06dc5c82892e054b631350378ad1beba46ddcc4b3b737b1283d0b89f415e1a62

Transactions (1)

Coinbase06dc5c82892e05…d0b89f415e1a62

1 in → 55 out10.0800 XPM1.89 KB

AMypZdXS…5jJKu8wP AdwTEXyC…NwbVbqZV ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC ARR7aRH6…ne3DXGXZ

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.

1.434 × 10⁹⁰(91-digit number)

14343057799944424813…14392998462669352319

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

1.434 × 10⁹⁰(91-digit number)

14343057799944424813…14392998462669352319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.434 × 10⁹⁰(91-digit number)

14343057799944424813…14392998462669352321

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

2.868 × 10⁹⁰(91-digit number)

28686115599888849626…28785996925338704639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.868 × 10⁹⁰(91-digit number)

28686115599888849626…28785996925338704641

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

5.737 × 10⁹⁰(91-digit number)

57372231199777699252…57571993850677409279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.737 × 10⁹⁰(91-digit number)

57372231199777699252…57571993850677409281

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

1.147 × 10⁹¹(92-digit number)

11474446239955539850…15143987701354818559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.147 × 10⁹¹(92-digit number)

11474446239955539850…15143987701354818561

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

2.294 × 10⁹¹(92-digit number)

22948892479911079700…30287975402709637119

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 #232,795

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