Block #269,158

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 8:08:04 PM · Difficulty 9.9547 · 6,526,852 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1907b12da88d92b3e83bbc4f84f253fc2ffae12090ff820df619a1cf24a4c7ea

View on Chainz ↗

Height

#269,158

Difficulty

9.954704

Transactions

Size

1.87 KB

Version

Bits

09f46774

Nonce

9,339

Timestamp

11/22/2013, 8:08:04 PM

Confirmations

6,526,852

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

1311bd47077313f4f096c1922d6b686a4a2d3a26f7a95dd5235f1736e987ea55

Transactions (4)

Coinbase54fd16a8743960…e8f73373ff4908

1 in → 1 out10.1200 XPM110 B

AeKNrjNj…1NEq95Ta

1980cb39a44f3e…e20950313c283f

1 in → 2 out5.0129 XPM226 B

AMMrwcYv…gfxpN49n AKdGpZUf…9vYFBTYv

bc971833f1cd49…111fbdcb733a48

8 in → 2 out1.0197 XPM1.24 KB

AcMcQnwv…6VkAydVM ARFWa3Yv…vEAGVDCt

82bb31a84b625b…f297094a0e3287

1 in → 2 out3.8909 XPM226 B

AdVBXEDX…iYYtZqNC AeKNrjNj…1NEq95Ta

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.

1.729 × 10⁹⁶(97-digit number)

17296925656956474203…25426109902383144959

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

1.729 × 10⁹⁶(97-digit number)

17296925656956474203…25426109902383144959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.729 × 10⁹⁶(97-digit number)

17296925656956474203…25426109902383144961

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

3.459 × 10⁹⁶(97-digit number)

34593851313912948406…50852219804766289919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.459 × 10⁹⁶(97-digit number)

34593851313912948406…50852219804766289921

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

6.918 × 10⁹⁶(97-digit number)

69187702627825896812…01704439609532579839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.918 × 10⁹⁶(97-digit number)

69187702627825896812…01704439609532579841

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

1.383 × 10⁹⁷(98-digit number)

13837540525565179362…03408879219065159679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.383 × 10⁹⁷(98-digit number)

13837540525565179362…03408879219065159681

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

2.767 × 10⁹⁷(98-digit number)

27675081051130358724…06817758438130319359

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