Block #572,825

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/2/2014, 8:32:16 AM · Difficulty 10.9663 · 6,238,227 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5d9294e1c911fa1b8e5abb5b93bd2b6a600f25da7d34997bdc65b0ea414d5cb8

View on Chainz ↗

Height

#572,825

Difficulty

10.966284

Transactions

Size

47.39 KB

Version

Bits

0af75e5d

Nonce

381,475,098

Timestamp

6/2/2014, 8:32:16 AM

Confirmations

6,238,227

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ca73e0c000b84eb94da2eb889b8446b727c02e1eb023cd5cd76b5b41db41128a

Transactions (2)

Coinbaseaca44ad8a9bef2…96757573c6e648

1 in → 1 out8.7900 XPM116 B

ANSXnLY2…Sd25TjkD

d0e025c256c18e…6090a74ff0103e

326 in → 2 out266.0105 XPM47.19 KB

AP16MtiY…j8y36fRd AMNiuZ5Z…EJwGgnJH

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.

1.457 × 10¹⁰¹(102-digit number)

14574437968827632672…87898531594539827199

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

1.457 × 10¹⁰¹(102-digit number)

14574437968827632672…87898531594539827199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.457 × 10¹⁰¹(102-digit number)

14574437968827632672…87898531594539827201

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

2.914 × 10¹⁰¹(102-digit number)

29148875937655265345…75797063189079654399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.914 × 10¹⁰¹(102-digit number)

29148875937655265345…75797063189079654401

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

5.829 × 10¹⁰¹(102-digit number)

58297751875310530691…51594126378159308799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.829 × 10¹⁰¹(102-digit number)

58297751875310530691…51594126378159308801

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

1.165 × 10¹⁰²(103-digit number)

11659550375062106138…03188252756318617599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.165 × 10¹⁰²(103-digit number)

11659550375062106138…03188252756318617601

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

2.331 × 10¹⁰²(103-digit number)

23319100750124212276…06376505512637235199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.331 × 10¹⁰²(103-digit number)

23319100750124212276…06376505512637235201

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 #572,825

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