Block #255,443

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/11/2013, 6:43:44 AM · Difficulty 9.9743 · 6,557,256 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9abd7e9ec9f1daf4a0a2ec88b5e256a2a3aba9f1dfd77aa95072f4b18235d44f

View on Chainz ↗

Height

#255,443

Difficulty

9.974265

Transactions

Size

1.77 KB

Version

Bits

09f96970

Nonce

31,640

Timestamp

11/11/2013, 6:43:44 AM

Confirmations

6,557,256

Mined by

⛏️ aR|tAL1mTAQVSpSFUT7A8YRHq3hqjTK5csEDoY

Merkle Root

37df025076cbe1e2cb9d4f5c042d765d0fad3be4f8c4afe1e4fe05301300426c

Transactions (1)

Coinbase37df025076cbe1…fe05301300426c

1 in → 49 out10.0200 XPM1.69 KB

AL1mTAQV…K5csEDoY ARHHafrz…e97CXM4q AQtzUSwq…htAuF3yC AUvzrouC…om76UcPR 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.

1.996 × 10⁸⁹(90-digit number)

19963068811400622838…22341414465208182439

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

1.996 × 10⁸⁹(90-digit number)

19963068811400622838…22341414465208182439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.996 × 10⁸⁹(90-digit number)

19963068811400622838…22341414465208182441

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

3.992 × 10⁸⁹(90-digit number)

39926137622801245677…44682828930416364879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.992 × 10⁸⁹(90-digit number)

39926137622801245677…44682828930416364881

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

7.985 × 10⁸⁹(90-digit number)

79852275245602491355…89365657860832729759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.985 × 10⁸⁹(90-digit number)

79852275245602491355…89365657860832729761

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

1.597 × 10⁹⁰(91-digit number)

15970455049120498271…78731315721665459519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.597 × 10⁹⁰(91-digit number)

15970455049120498271…78731315721665459521

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

3.194 × 10⁹⁰(91-digit number)

31940910098240996542…57462631443330919039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.194 × 10⁹⁰(91-digit number)

31940910098240996542…57462631443330919041

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 #255,443

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