Block #426,171

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 10:46:33 AM · Difficulty 10.3583 · 6,384,719 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d6315e5d07963d1608210693066779d46cc19407b7ae431e464b6f3bd31a29a

View on Chainz ↗

Height

#426,171

Difficulty

10.358288

Transactions

Size

24.98 KB

Version

Bits

0a5bb8c0

Nonce

13,160

Timestamp

3/2/2014, 10:46:33 AM

Confirmations

6,384,719

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f236ea9da163de092ff6e11483701279fc9fb19be9dc5789eb9c98c0d8aeefbe

Transactions (4)

Coinbase8bdd9b8aac14a7…77d24d9cdebbbc

1 in → 23 out9.3100 XPM845 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

ac1a6b444b86c6…89962e12710109

156 in → 2 out54.0552 XPM22.63 KB

AHh4bg8h…1ZiCW3y5 AXR4TwBC…u4VAEto3

7b22333ce3cf89…6bbf90d00742b4

6 in → 10 out29.3325 XPM1.11 KB

ALzEcqtK…Kqba6hiT AJTnJPkG…6HTSvS8F AcBnBiUw…CYFN81QZ AMurAYrb…3iomaSF2 AcADmAoe…8iNnoMzB

bd2d01efb33761…f893656051bf93

2 in → 1 out6.1242 XPM341 B

APhyxg3g…LNqfRJSZ

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.

7.141 × 10⁹⁸(99-digit number)

71419205668161383437…70628306991716643719

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

7.141 × 10⁹⁸(99-digit number)

71419205668161383437…70628306991716643719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.141 × 10⁹⁸(99-digit number)

71419205668161383437…70628306991716643721

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

1.428 × 10⁹⁹(100-digit number)

14283841133632276687…41256613983433287439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.428 × 10⁹⁹(100-digit number)

14283841133632276687…41256613983433287441

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

2.856 × 10⁹⁹(100-digit number)

28567682267264553375…82513227966866574879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.856 × 10⁹⁹(100-digit number)

28567682267264553375…82513227966866574881

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

5.713 × 10⁹⁹(100-digit number)

57135364534529106750…65026455933733149759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.713 × 10⁹⁹(100-digit number)

57135364534529106750…65026455933733149761

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

1.142 × 10¹⁰⁰(101-digit number)

11427072906905821350…30052911867466299519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.142 × 10¹⁰⁰(101-digit number)

11427072906905821350…30052911867466299521

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 #426,171

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