Block #364,443

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2014, 2:00:03 AM · Difficulty 10.4213 · 6,466,329 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6bb9d6dc726ba1a80e4dd22bcaed8c0cbca487b10182fbb1d1a83b96d8c9c966

View on Chainz ↗

Height

#364,443

Difficulty

10.421292

Transactions

Size

579 B

Version

Bits

0a6bd9c4

Nonce

1,346

Timestamp

1/18/2014, 2:00:03 AM

Confirmations

6,466,329

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

3244b4713ce03db0f76817acf06fcb2fc1b3d65668cc9a1784128e27c26ea8ee

Transactions (2)

Coinbasefc783ba9b35bea…9e97d9918fa522

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

efba146f19f50f…3e2df354cb717f

2 in → 2 out10.0182 XPM374 B

AdbghLi9…eT6v18Uy AWXCqPbG…i2fD6hjj

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.

2.465 × 10⁹¹(92-digit number)

24656612681712733659…61069708240961964379

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

2.465 × 10⁹¹(92-digit number)

24656612681712733659…61069708240961964379

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.465 × 10⁹¹(92-digit number)

24656612681712733659…61069708240961964381

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

4.931 × 10⁹¹(92-digit number)

49313225363425467318…22139416481923928759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.931 × 10⁹¹(92-digit number)

49313225363425467318…22139416481923928761

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

9.862 × 10⁹¹(92-digit number)

98626450726850934636…44278832963847857519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.862 × 10⁹¹(92-digit number)

98626450726850934636…44278832963847857521

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

1.972 × 10⁹²(93-digit number)

19725290145370186927…88557665927695715039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.972 × 10⁹²(93-digit number)

19725290145370186927…88557665927695715041

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

3.945 × 10⁹²(93-digit number)

39450580290740373854…77115331855391430079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.945 × 10⁹²(93-digit number)

39450580290740373854…77115331855391430081

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 #364,443

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