Block #251,579

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 3:02:40 AM · Difficulty 9.9700 · 6,592,859 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8fb2afff3946bd2f695808bf18268f21f6fc5b2097485692ca4adcc4edfa36db

View on Chainz ↗

Height

#251,579

Difficulty

9.969994

Transactions

Size

2.11 KB

Version

Bits

09f85182

Nonce

56,270

Timestamp

11/9/2013, 3:02:40 AM

Confirmations

6,592,859

Mined by

⛏️ aR}AKwcMAcHMxC6hzN9c8RsVfpBWrWGekVdtp

Merkle Root

cde9d121976ccb9e721c96cec54f90f68dc4fb45860b0208c5516024064c41de

Transactions (1)

Coinbasecde9d121976ccb…516024064c41de

1 in → 59 out10.0200 XPM2.02 KB

AKwcMAcH…WGekVdtp AeLaP1NX…SJ53Q2G7 AabHNb1B…GRoingRy AQtzUSwq…htAuF3yC AJKYzp1g…SvZiepke

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.

1.432 × 10⁸⁹(90-digit number)

14329748793023859593…54900332848502023039

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

1.432 × 10⁸⁹(90-digit number)

14329748793023859593…54900332848502023039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.432 × 10⁸⁹(90-digit number)

14329748793023859593…54900332848502023041

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

2.865 × 10⁸⁹(90-digit number)

28659497586047719186…09800665697004046079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.865 × 10⁸⁹(90-digit number)

28659497586047719186…09800665697004046081

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

5.731 × 10⁸⁹(90-digit number)

57318995172095438372…19601331394008092159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.731 × 10⁸⁹(90-digit number)

57318995172095438372…19601331394008092161

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

1.146 × 10⁹⁰(91-digit number)

11463799034419087674…39202662788016184319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.146 × 10⁹⁰(91-digit number)

11463799034419087674…39202662788016184321

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

2.292 × 10⁹⁰(91-digit number)

22927598068838175348…78405325576032368639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.292 × 10⁹⁰(91-digit number)

22927598068838175348…78405325576032368641

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 #251,579

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