Block #500,505

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/19/2014, 4:57:17 AM · Difficulty 10.8003 · 6,308,449 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e30432482bb94b33886998eb7d437d828ad43755434bab238b0a48738f866427

View on Chainz ↗

Height

#500,505

Difficulty

10.800331

Transactions

Size

1.41 KB

Version

Bits

0acce276

Nonce

324,297,394

Timestamp

4/19/2014, 4:57:17 AM

Confirmations

6,308,449

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

1ba52c4930cd5dd588c0b2b749f7cfaa34dd27b1d057005bbc4a6a938326c8a8

Transactions (5)

Coinbasee107da67e39faa…2dbf9de8b7b155

1 in → 1 out8.6000 XPM116 B

AbwWkWZt…kawDhufa

25781e10384c37…cfed8a13d16b6e

2 in → 2 out12.3077 XPM374 B

AFp8131R…6QhaAMBz AZwg5w3M…b3189Zf8

8269e9404c474b…61690fc91be2c8

2 in → 5 out17.2800 XPM407 B

AM6JvF6Y…u5DULnSo AXy8CJrT…rHLoyh3A ALAnEiVB…xvH3QqUj AcBvLaSu…X3gaHvJ1 AeKNrjNj…1NEq95Ta

76d57d9f89d1d5…b41e9e693ab27c

1 in → 2 out6.1212 XPM225 B

AH52Hq4j…Vvrpm7zy AXgLqQr9…cv78kqER

5b0d150965692b…d85fb046f90c89

1 in → 2 out5.8863 XPM225 B

APLQsbmU…RHbxjXyy ASv3FuVy…Sr7zJ82t

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.

2.571 × 10⁹⁹(100-digit number)

25716659573280015549…59705668532001318399

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

2.571 × 10⁹⁹(100-digit number)

25716659573280015549…59705668532001318399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.571 × 10⁹⁹(100-digit number)

25716659573280015549…59705668532001318401

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

5.143 × 10⁹⁹(100-digit number)

51433319146560031099…19411337064002636799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.143 × 10⁹⁹(100-digit number)

51433319146560031099…19411337064002636801

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

1.028 × 10¹⁰⁰(101-digit number)

10286663829312006219…38822674128005273599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.028 × 10¹⁰⁰(101-digit number)

10286663829312006219…38822674128005273601

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

2.057 × 10¹⁰⁰(101-digit number)

20573327658624012439…77645348256010547199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.057 × 10¹⁰⁰(101-digit number)

20573327658624012439…77645348256010547201

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

4.114 × 10¹⁰⁰(101-digit number)

41146655317248024879…55290696512021094399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.114 × 10¹⁰⁰(101-digit number)

41146655317248024879…55290696512021094401

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 #500,505

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