Block #468,095

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2014, 6:49:18 AM · Difficulty 10.4311 · 6,336,098 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

55b3661f60dc2fda3ad5ca8d7c54182905143c60e7e1a83bfada85427aaabc21

View on Chainz ↗

Height

#468,095

Difficulty

10.431071

Transactions

Size

1.09 KB

Version

Bits

0a6e5ab1

Nonce

7,775

Timestamp

3/31/2014, 6:49:18 AM

Confirmations

6,336,098

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

864160b2cbcf4b955a3c18de7ca921aeaf92122bb7e6fc5805c8744281cda83f

Transactions (5)

Coinbased05477e581983f…649fdb15b1faea

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

50c4ac5faba81a…f017f80b11e2f2

1 in → 2 out6.6365 XPM226 B

AbEHpita…RpeBpsSe AYYuXBhL…FAH8rqCY

b17074840ce5ed…6c0526f1cfbcdf

1 in → 2 out5.1485 XPM225 B

AZqdRa8k…QFBQ9ZyL AQtisFei…VwsPGKH9

9bfd4cb04aa61d…0c3ff9c2ee5009

1 in → 2 out5.5398 XPM227 B

AM3QvEg1…ZooDjPcS AdMzUrLG…ewJSjLyd

ce68260a305a26…9939a00e831329

1 in → 2 out4.0763 XPM227 B

AMp27CcF…Zc4Vr7Uk AW7k2MZd…9b8YznyG

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.

1.434 × 10⁹⁷(98-digit number)

14348131989179925263…16036147442853167259

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

1.434 × 10⁹⁷(98-digit number)

14348131989179925263…16036147442853167259

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.434 × 10⁹⁷(98-digit number)

14348131989179925263…16036147442853167261

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

2.869 × 10⁹⁷(98-digit number)

28696263978359850527…32072294885706334519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.869 × 10⁹⁷(98-digit number)

28696263978359850527…32072294885706334521

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

5.739 × 10⁹⁷(98-digit number)

57392527956719701054…64144589771412669039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.739 × 10⁹⁷(98-digit number)

57392527956719701054…64144589771412669041

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

1.147 × 10⁹⁸(99-digit number)

11478505591343940210…28289179542825338079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.147 × 10⁹⁸(99-digit number)

11478505591343940210…28289179542825338081

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

2.295 × 10⁹⁸(99-digit number)

22957011182687880421…56578359085650676159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.295 × 10⁹⁸(99-digit number)

22957011182687880421…56578359085650676161

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