Block #329,092

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/25/2013, 5:36:20 PM · Difficulty 10.1710 · 6,469,249 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5c3cea4c51f2143c1bf01e804f985491a23e46249f061b56d8b5c0b776dc9099

View on Chainz ↗

Height

#329,092

Difficulty

10.170995

Transactions

Size

2.83 KB

Version

Bits

0a2bc64d

Nonce

343,810

Timestamp

12/25/2013, 5:36:20 PM

Confirmations

6,469,249

Mined by

⛏️ aRAKwqFUdzFNyMbekqhPUpd29CZJD4jGNKFN

Merkle Root

181e616a3c5fbe0179b2d98279d654dd7fd90c3e25c0987c76170bfdca7fe6b2

Transactions (4)

Coinbase60461958e61682…d867bd0f79c529

1 in → 26 out9.6500 XPM947 B

AKwqFUdz…D4jGNKFN APq822KM…wD9srp4m Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1

2d56d8fcb4c506…3306663293577a

4 in → 2 out151.9993 XPM670 B

AeFT24Di…UG6nJauN AaDT7rp4…5PevsrW6

44fceff02a368f…69d16566aef239

6 in → 2 out18.4402 XPM967 B

AJgHBdDN…EvnLDCYj Abf9NjUL…FDdauDyK

4e085d0fb76eb8…6f4fafa1137ce6

1 in → 2 out7.5512 XPM225 B

AUFxANzC…wSxXZx69 ATStVu26…QGpmNZva

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.

2.502 × 10⁹⁰(91-digit number)

25027074883587095838…91361358427325542119

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

2.502 × 10⁹⁰(91-digit number)

25027074883587095838…91361358427325542119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.502 × 10⁹⁰(91-digit number)

25027074883587095838…91361358427325542121

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

5.005 × 10⁹⁰(91-digit number)

50054149767174191676…82722716854651084239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.005 × 10⁹⁰(91-digit number)

50054149767174191676…82722716854651084241

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

1.001 × 10⁹¹(92-digit number)

10010829953434838335…65445433709302168479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.001 × 10⁹¹(92-digit number)

10010829953434838335…65445433709302168481

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

2.002 × 10⁹¹(92-digit number)

20021659906869676670…30890867418604336959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.002 × 10⁹¹(92-digit number)

20021659906869676670…30890867418604336961

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

4.004 × 10⁹¹(92-digit number)

40043319813739353340…61781734837208673919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.004 × 10⁹¹(92-digit number)

40043319813739353340…61781734837208673921

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