Block #485,373

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/11/2014, 12:40:27 AM · Difficulty 10.6077 · 6,328,839 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

023c978dad49d80df32b4a7cd756fe3db95d9b0f31b5aa738cd63062ab0f8db0

View on Chainz ↗

Height

#485,373

Difficulty

10.607653

Transactions

Size

1.04 KB

Version

Bits

0a9b8f2a

Nonce

2,278,668

Timestamp

4/11/2014, 12:40:27 AM

Confirmations

6,328,839

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

cbeb491a6b8fdf9fd8f677a096cc05ee331d3769eacc209af519d97f2b8312a1

Transactions (3)

Coinbaseed475c3af54b28…bb5983907519e1

1 in → 1 out8.8900 XPM116 B

AbwWkWZt…kawDhufa

004a864fa787cd…5fa38f32889d3e

3 in → 2 out11.3359 XPM487 B

AeDapqMr…jgVQuugs AVP8FPuB…ByyT3npV

7b9155cf2d9333…99826e891e63ad

2 in → 2 out5.0711 XPM373 B

AU1JdeGU…anzPHLCa AGCmTSw4…QNSsCSPC

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.

1.443 × 10¹⁰⁰(101-digit number)

14432029398205379594…86912558647358382079

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

1.443 × 10¹⁰⁰(101-digit number)

14432029398205379594…86912558647358382079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.443 × 10¹⁰⁰(101-digit number)

14432029398205379594…86912558647358382081

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

2.886 × 10¹⁰⁰(101-digit number)

28864058796410759188…73825117294716764159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.886 × 10¹⁰⁰(101-digit number)

28864058796410759188…73825117294716764161

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

5.772 × 10¹⁰⁰(101-digit number)

57728117592821518376…47650234589433528319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.772 × 10¹⁰⁰(101-digit number)

57728117592821518376…47650234589433528321

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

1.154 × 10¹⁰¹(102-digit number)

11545623518564303675…95300469178867056639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.154 × 10¹⁰¹(102-digit number)

11545623518564303675…95300469178867056641

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

2.309 × 10¹⁰¹(102-digit number)

23091247037128607350…90600938357734113279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.309 × 10¹⁰¹(102-digit number)

23091247037128607350…90600938357734113281

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 #485,373

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