Block #215,382

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 1:21:40 AM · Difficulty 9.9254 · 6,583,983 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dff876b0368619dc17228afbf4bb47490b1532c00a283709f125917bdd08e86a

View on Chainz ↗

Height

#215,382

Difficulty

9.925429

Transactions

Size

5.83 KB

Version

Bits

09ece8ed

Nonce

1,164,773,213

Timestamp

10/18/2013, 1:21:40 AM

Confirmations

6,583,983

Mined by

⛏️ VIR`oAdWSNMJhcuCmqvvd3ppX8wXDhjRSr2Ldse

Merkle Root

77a65b1436a2b83a368f8f2e567893d621b2b7ef9c559842302406ea9bffd6cb

Transactions (1)

Coinbase77a65b1436a2b8…2406ea9bffd6cb

1 in → 171 out10.0800 XPM5.74 KB

AdWSNMJh…RSr2Ldse AN2qwcH9…bHEfHtFq AZ4FA5yw…ZaN9qBvU AGaKkABV…XGSDBNzn AehSbrXS…x2Vu99iu

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.

5.979 × 10⁹¹(92-digit number)

59794867370932771439…57960748703238478719

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

5.979 × 10⁹¹(92-digit number)

59794867370932771439…57960748703238478719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.979 × 10⁹¹(92-digit number)

59794867370932771439…57960748703238478721

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

1.195 × 10⁹²(93-digit number)

11958973474186554287…15921497406476957439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.195 × 10⁹²(93-digit number)

11958973474186554287…15921497406476957441

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

2.391 × 10⁹²(93-digit number)

23917946948373108575…31842994812953914879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.391 × 10⁹²(93-digit number)

23917946948373108575…31842994812953914881

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

4.783 × 10⁹²(93-digit number)

47835893896746217151…63685989625907829759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.783 × 10⁹²(93-digit number)

47835893896746217151…63685989625907829761

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

9.567 × 10⁹²(93-digit number)

95671787793492434303…27371979251815659519

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