Block #344,471

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/5/2014, 8:12:11 AM · Difficulty 10.1932 · 6,454,401 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0ddc957470479d16171c644e2d3117df198779791c772a4aa71a92011f6ef0d2

View on Chainz ↗

Height

#344,471

Difficulty

10.193224

Transactions

Size

1.11 KB

Version

Bits

0a317719

Nonce

32,686

Timestamp

1/5/2014, 8:12:11 AM

Confirmations

6,454,401

Mined by

⛏️ AaRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c124834e3321d61180ae48719a7c22e8ac72b6516d370e8860733964fa18f380

Transactions (1)

Coinbasec124834e3321d6…733964fa18f380

1 in → 29 out9.5900 XPM1.02 KB

AQvZBsUo…hppgRZTJ Ad9pSzHt…cpJ3y2zz AJLB8H7s…MRD4s5wA AYtDvcGs…VuAcA7m7 ATv3Pbhq…4aHz5j1G

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.

7.195 × 10⁹⁷(98-digit number)

71958256693343906054…42870953795879199359

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

7.195 × 10⁹⁷(98-digit number)

71958256693343906054…42870953795879199359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.195 × 10⁹⁷(98-digit number)

71958256693343906054…42870953795879199361

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

1.439 × 10⁹⁸(99-digit number)

14391651338668781210…85741907591758398719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.439 × 10⁹⁸(99-digit number)

14391651338668781210…85741907591758398721

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

2.878 × 10⁹⁸(99-digit number)

28783302677337562421…71483815183516797439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.878 × 10⁹⁸(99-digit number)

28783302677337562421…71483815183516797441

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

5.756 × 10⁹⁸(99-digit number)

57566605354675124843…42967630367033594879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.756 × 10⁹⁸(99-digit number)

57566605354675124843…42967630367033594881

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

1.151 × 10⁹⁹(100-digit number)

11513321070935024968…85935260734067189759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.151 × 10⁹⁹(100-digit number)

11513321070935024968…85935260734067189761

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