Block #492,462

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/15/2014, 3:56:43 AM · Difficulty 10.6878 · 6,318,262 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

93ed66010f77525bae720a9ee174b753516b40b57fb2f6263f8c466a6bb8d316

View on Chainz ↗

Height

#492,462

Difficulty

10.687831

Transactions

Size

43.37 KB

Version

Bits

0ab015ab

Nonce

43,428

Timestamp

4/15/2014, 3:56:43 AM

Confirmations

6,318,262

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

1d3fa9cc449fc63618817aed7bb9ffa09a29c922e872ce8b1bcfde4ceb606b94

Transactions (3)

Coinbase0ed3726a34893a…3eb994d40a19c9

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

89951eb44893e2…3c3284fc231881

25 in → 1 out12.5586 XPM3.66 KB

AY4QThR8…j5XjHR2Z

fb69e7331dccb3…0169ce526b2b64

273 in → 2 out500.0100 XPM39.51 KB

AJjnK9uC…VreFquR4 ATgPDptW…2JnYcQZP

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.

3.642 × 10¹⁰¹(102-digit number)

36425511370694825209…63306984147566076159

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

3.642 × 10¹⁰¹(102-digit number)

36425511370694825209…63306984147566076159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.642 × 10¹⁰¹(102-digit number)

36425511370694825209…63306984147566076161

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

7.285 × 10¹⁰¹(102-digit number)

72851022741389650418…26613968295132152319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.285 × 10¹⁰¹(102-digit number)

72851022741389650418…26613968295132152321

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

1.457 × 10¹⁰²(103-digit number)

14570204548277930083…53227936590264304639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.457 × 10¹⁰²(103-digit number)

14570204548277930083…53227936590264304641

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

2.914 × 10¹⁰²(103-digit number)

29140409096555860167…06455873180528609279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.914 × 10¹⁰²(103-digit number)

29140409096555860167…06455873180528609281

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

5.828 × 10¹⁰²(103-digit number)

58280818193111720335…12911746361057218559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.828 × 10¹⁰²(103-digit number)

58280818193111720335…12911746361057218561

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 #492,462

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