Block #2,539,716

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/26/2018, 5:48:02 PM · Difficulty 10.9870 · 4,305,483 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

394cf2ee52c3f9ceb3f84386f100749473895d12488f2d6ec68d0e48e94603a4

View on Chainz ↗

Height

#2,539,716

Difficulty

10.987007

Transactions

Size

38.35 KB

Version

Bits

0afcac83

Nonce

967,481,826

Timestamp

2/26/2018, 5:48:02 PM

Confirmations

4,305,483

Mined by

⛏️ P2SHAeryxTkC8awrFUMKyzqB1ifzRH1FyFFVVM

Merkle Root

a19ec0fd287fb14179547a84b8d1187088dd074e98fdaeadf717cf71a708d111

Transactions (3)

Coinbase580d5f7901e566…ca69d7c2bff0e1

1 in → 1 out8.6700 XPM110 B

AeryxTkC…1FyFFVVM

b61bbfcfe78e98…a838bbc6074cbe

91 in → 2 out372.0110 XPM13.23 KB

APxGQgiM…5Vf6tgzE AGW8iVgz…xMg7SUHX

a5244f71eab59f…c86c57abe067e5

172 in → 2 out688.3900 XPM24.92 KB

AWS9JMzG…zgfH3nXC AVohzkuG…s5PN1EEw

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.

5.527 × 10⁹⁴(95-digit number)

55272250916837837541…81810470571179191359

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

5.527 × 10⁹⁴(95-digit number)

55272250916837837541…81810470571179191359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.527 × 10⁹⁴(95-digit number)

55272250916837837541…81810470571179191361

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

1.105 × 10⁹⁵(96-digit number)

11054450183367567508…63620941142358382719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.105 × 10⁹⁵(96-digit number)

11054450183367567508…63620941142358382721

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

2.210 × 10⁹⁵(96-digit number)

22108900366735135016…27241882284716765439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.210 × 10⁹⁵(96-digit number)

22108900366735135016…27241882284716765441

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

4.421 × 10⁹⁵(96-digit number)

44217800733470270033…54483764569433530879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.421 × 10⁹⁵(96-digit number)

44217800733470270033…54483764569433530881

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

8.843 × 10⁹⁵(96-digit number)

88435601466940540066…08967529138867061759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.843 × 10⁹⁵(96-digit number)

88435601466940540066…08967529138867061761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.768 × 10⁹⁶(97-digit number)

17687120293388108013…17935058277734123519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,539,716

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