Home/Chain Registry/Block #272,305

Block #272,305

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 4:40:30 AM · Difficulty 9.9526 · 6,519,054 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e1c57acbd4cdbeea76ef16345ba79b0a22f2887ab0206a9b490f751ded23e81

View on Chainz ↗

Height

#272,305

Difficulty

9.952565

Transactions

Size

729 B

Version

Bits

09f3db47

Nonce

136,484

Timestamp

11/25/2013, 4:40:30 AM

Confirmations

6,519,054

Merkle Root

d170cfb48997c9c321691785a07d25d82c5027475d780eadca29d1ccd1e25a70

Transactions (1)

Coinbased170cfb48997c9…29d1ccd1e25a70

1 in → 17 out10.0800 XPM641 B

AJaGRnaj…iCHGoy6E AexKjVEe…phmLMPem ARanXFdq…2FNquU2w ANuKx9Ke…wm7nrBRq ALbcgZi8…cmdXkNVF

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.

3.446 × 10⁹⁰(91-digit number)

34468995797028306231…69330625969300390440

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

3.446 × 10⁹⁰(91-digit number)

34468995797028306231…69330625969300390439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.446 × 10⁹⁰(91-digit number)

34468995797028306231…69330625969300390441

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

6.893 × 10⁹⁰(91-digit number)

68937991594056612462…38661251938600780879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.893 × 10⁹⁰(91-digit number)

68937991594056612462…38661251938600780881

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

1.378 × 10⁹¹(92-digit number)

13787598318811322492…77322503877201561759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.378 × 10⁹¹(92-digit number)

13787598318811322492…77322503877201561761

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

2.757 × 10⁹¹(92-digit number)

27575196637622644984…54645007754403123519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.757 × 10⁹¹(92-digit number)

27575196637622644984…54645007754403123521

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

5.515 × 10⁹¹(92-digit number)

55150393275245289969…09290015508806247039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.515 × 10⁹¹(92-digit number)

55150393275245289969…09290015508806247041

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.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 272305

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 5e1c57acbd4cdbeea76ef16345ba79b0a22f2887ab0206a9b490f751ded23e81

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #272,305 on Chainz ↗