Block #509,548

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/25/2014, 3:15:47 AM · Difficulty 10.8202 · 6,297,272 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bc245cc342cf5cce6c2ede249e5dfae2b6f4f862fb15f45e2cc9f41e3ea9a530

View on Chainz ↗

Height

#509,548

Difficulty

10.820227

Transactions

Size

1.08 KB

Version

Bits

0ad1fa62

Nonce

27,674,631

Timestamp

4/25/2014, 3:15:47 AM

Confirmations

6,297,272

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

90d6e448140892d3212af1ff60cedb5c5856ef568c3b07c2182c0a04b54ac609

Transactions (3)

Coinbase684e1a8e036a64…ab8f0f2e32af06

1 in → 1 out8.5500 XPM116 B

AbwWkWZt…kawDhufa

69e281dfe5b24a…c784d483ae71a4

4 in → 2 out20.0159 XPM671 B

AeyxVBxK…Q5bS1qhZ AUmEdQzk…u6XbrMTL

fda17a04c24910…109f220adb02ee

1 in → 3 out8.5300 XPM225 B

AWq6vDNx…FMFpMcN1 APRxG4Vc…GZqmXrSs AeKNrjNj…1NEq95Ta

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.

5.267 × 10¹⁰⁰(101-digit number)

52676812015527781378…84280675097324720639

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

5.267 × 10¹⁰⁰(101-digit number)

52676812015527781378…84280675097324720639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.267 × 10¹⁰⁰(101-digit number)

52676812015527781378…84280675097324720641

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

1.053 × 10¹⁰¹(102-digit number)

10535362403105556275…68561350194649441279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.053 × 10¹⁰¹(102-digit number)

10535362403105556275…68561350194649441281

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

2.107 × 10¹⁰¹(102-digit number)

21070724806211112551…37122700389298882559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.107 × 10¹⁰¹(102-digit number)

21070724806211112551…37122700389298882561

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

4.214 × 10¹⁰¹(102-digit number)

42141449612422225102…74245400778597765119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.214 × 10¹⁰¹(102-digit number)

42141449612422225102…74245400778597765121

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

8.428 × 10¹⁰¹(102-digit number)

84282899224844450205…48490801557195530239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.428 × 10¹⁰¹(102-digit number)

84282899224844450205…48490801557195530241

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 #509,548

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