Block #363,136

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/17/2014, 5:07:47 AM · Difficulty 10.4141 · 6,463,358 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

36676727bdd894e82c93f46f0dafe4274da47611f32cf22b8b223d19ce2caa6c

View on Chainz ↗

Height

#363,136

Difficulty

10.414078

Transactions

Size

1.02 KB

Version

Bits

0a6a0107

Nonce

301,989,922

Timestamp

1/17/2014, 5:07:47 AM

Confirmations

6,463,358

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

2b0024e870e4f7030e2f1d319087172bdb40c34a2ab95614e9a09426f64c6595

Transactions (2)

Coinbase96fe12c734b403…33299432552e74

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

079aad95af645a…e4c7490c9f694c

4 in → 10 out28.8469 XPM839 B

Abbg2x1q…5rBwNn93 ATE8kUTd…Fdv2WBkq AZZ9mXy8…bVJfUD26 AK2c7Mwr…iVRQjN8q AZH3aBJB…T7FVgZ83

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.

7.967 × 10⁹⁵(96-digit number)

79677156075939738418…56103358305586882399

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

7.967 × 10⁹⁵(96-digit number)

79677156075939738418…56103358305586882399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.967 × 10⁹⁵(96-digit number)

79677156075939738418…56103358305586882401

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

1.593 × 10⁹⁶(97-digit number)

15935431215187947683…12206716611173764799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.593 × 10⁹⁶(97-digit number)

15935431215187947683…12206716611173764801

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

3.187 × 10⁹⁶(97-digit number)

31870862430375895367…24413433222347529599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.187 × 10⁹⁶(97-digit number)

31870862430375895367…24413433222347529601

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

6.374 × 10⁹⁶(97-digit number)

63741724860751790734…48826866444695059199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.374 × 10⁹⁶(97-digit number)

63741724860751790734…48826866444695059201

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

1.274 × 10⁹⁷(98-digit number)

12748344972150358146…97653732889390118399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.274 × 10⁹⁷(98-digit number)

12748344972150358146…97653732889390118401

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 #363,136

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