Home/Chain Registry/Block #285,241

Block #285,241

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 10:28:26 AM · Difficulty 9.9840 · 6,515,355 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

00bd5bd110b8ec7e057b287b052e4ad3caeab25624cdded55d20c7d8f3a11344

View on Chainz ↗

Height

#285,241

Difficulty

9.983963

Transactions

Size

213 B

Version

Bits

09fbe4fe

Nonce

646

Timestamp

11/30/2013, 10:28:26 AM

Confirmations

6,515,355

Merkle Root

c148847d6d9c2e4c8715f6e63392ad45c94c772a132a597abe832ad67e724b54

Transactions (1)

Coinbasec148847d6d9c2e…832ad67e724b54

1 in → 1 out10.0200 XPM116 B

AcLBm5Z9…S683d7c3

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.

3.078 × 10¹¹²(113-digit number)

30786856288758983072…38426024783081635840

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

3.078 × 10¹¹²(113-digit number)

30786856288758983072…38426024783081635839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.078 × 10¹¹²(113-digit number)

30786856288758983072…38426024783081635841

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

6.157 × 10¹¹²(113-digit number)

61573712577517966145…76852049566163271679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.157 × 10¹¹²(113-digit number)

61573712577517966145…76852049566163271681

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

1.231 × 10¹¹³(114-digit number)

12314742515503593229…53704099132326543359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.231 × 10¹¹³(114-digit number)

12314742515503593229…53704099132326543361

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

2.462 × 10¹¹³(114-digit number)

24629485031007186458…07408198264653086719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.462 × 10¹¹³(114-digit number)

24629485031007186458…07408198264653086721

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

4.925 × 10¹¹³(114-digit number)

49258970062014372916…14816396529306173439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.925 × 10¹¹³(114-digit number)

49258970062014372916…14816396529306173441

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 285241

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 00bd5bd110b8ec7e057b287b052e4ad3caeab25624cdded55d20c7d8f3a11344

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 #285,241 on Chainz ↗