Block #482,177

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/9/2014, 8:27:51 AM · Difficulty 10.5409 · 6,334,631 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb29cb1af0ee8e08d27b603d4645cbc21ad765f1a82eaf926b00bec35bf94354

View on Chainz ↗

Height

#482,177

Difficulty

10.540895

Transactions

Size

427 B

Version

Bits

0a8a781b

Nonce

17,950,030

Timestamp

4/9/2014, 8:27:51 AM

Confirmations

6,334,631

Mined by

⛏️ P2SHAJS1GYK9N4E66pfvSME3sQSSYL8RpnV4NK

Merkle Root

ce83f5b44346204402bc3c2168413e49a532bbf2a135aeab67a28fab4348d41c

Transactions (2)

Coinbasea17126cf3d0371…5dc87e28918149

1 in → 1 out9.0000 XPM109 B

AJS1GYK9…8RpnV4NK

092e9e57203bed…62514563abd569

1 in → 2 out1.9093 XPM226 B

AVLSWwcb…wMB7xpNU Ac24WwPt…BSeTbxUj

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.

5.680 × 10⁹⁸(99-digit number)

56809832045930352443…95084334538338959359

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

5.680 × 10⁹⁸(99-digit number)

56809832045930352443…95084334538338959359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.680 × 10⁹⁸(99-digit number)

56809832045930352443…95084334538338959361

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

1.136 × 10⁹⁹(100-digit number)

11361966409186070488…90168669076677918719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.136 × 10⁹⁹(100-digit number)

11361966409186070488…90168669076677918721

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

2.272 × 10⁹⁹(100-digit number)

22723932818372140977…80337338153355837439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.272 × 10⁹⁹(100-digit number)

22723932818372140977…80337338153355837441

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

4.544 × 10⁹⁹(100-digit number)

45447865636744281954…60674676306711674879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.544 × 10⁹⁹(100-digit number)

45447865636744281954…60674676306711674881

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

9.089 × 10⁹⁹(100-digit number)

90895731273488563909…21349352613423349759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.089 × 10⁹⁹(100-digit number)

90895731273488563909…21349352613423349761

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 #482,177

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