Block #232,141

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/28/2013, 10:06:03 PM · Difficulty 9.9410 · 6,584,784 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

337d71098d16b7cb9e4f292ede3b6cd71bb1d057b8f00c53df2cb3003c8a1f1a

View on Chainz ↗

Height

#232,141

Difficulty

9.940974

Transactions

Size

2.40 KB

Version

Bits

09f0e3af

Nonce

266

Timestamp

10/28/2013, 10:06:03 PM

Confirmations

6,584,784

Mined by

⛏️ Rn\AU9KdB9rpz9LAxy9pEhEHibVcuo5XC6WMy

Merkle Root

9a2637af1f2af1d3e386ac08dcabc066a10d56c2b5ce2b2fa3011ed215dba560

Transactions (1)

Coinbase9a2637af1f2af1…011ed215dba560

1 in → 68 out10.0700 XPM2.32 KB

AU9KdB9r…o5XC6WMy ANuKx9Ke…wm7nrBRq AMVsYFfp…DB9jn4fb AHY1L1zP…op3KHdyK AJaGRnaj…iCHGoy6E

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.

1.917 × 10⁹⁰(91-digit number)

19177793383497117046…01799034402421200459

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

1.917 × 10⁹⁰(91-digit number)

19177793383497117046…01799034402421200459

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.917 × 10⁹⁰(91-digit number)

19177793383497117046…01799034402421200461

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

3.835 × 10⁹⁰(91-digit number)

38355586766994234092…03598068804842400919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.835 × 10⁹⁰(91-digit number)

38355586766994234092…03598068804842400921

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

7.671 × 10⁹⁰(91-digit number)

76711173533988468185…07196137609684801839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.671 × 10⁹⁰(91-digit number)

76711173533988468185…07196137609684801841

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

1.534 × 10⁹¹(92-digit number)

15342234706797693637…14392275219369603679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.534 × 10⁹¹(92-digit number)

15342234706797693637…14392275219369603681

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

3.068 × 10⁹¹(92-digit number)

30684469413595387274…28784550438739207359

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 #232,141

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