Home/Chain Registry/Block #499,245

Block #499,245

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/18/2014, 12:26:47 PM · Difficulty 10.7892 · 6,301,608 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c08cc65d1d946d76248f77b7bde0a16221a79f80e6598efdf33c2a571a6810dd

View on Chainz ↗

Height

#499,245

Difficulty

10.789151

Transactions

Size

214 B

Version

Bits

0aca05cb

Nonce

23,388

Timestamp

4/18/2014, 12:26:47 PM

Confirmations

6,301,608

Merkle Root

ed8744b0d7e8141c05e1d00a6af240f7879b719f2df5fdf9131030ddf763f18f

Transactions (1)

Coinbaseed8744b0d7e814…1030ddf763f18f

1 in → 1 out8.5800 XPM116 B

AbwWkWZt…kawDhufa

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.

4.806 × 10¹¹³(114-digit number)

48065587108792582587…03094973788637498560

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

4.806 × 10¹¹³(114-digit number)

48065587108792582587…03094973788637498559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.806 × 10¹¹³(114-digit number)

48065587108792582587…03094973788637498561

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

9.613 × 10¹¹³(114-digit number)

96131174217585165175…06189947577274997119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.613 × 10¹¹³(114-digit number)

96131174217585165175…06189947577274997121

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

1.922 × 10¹¹⁴(115-digit number)

19226234843517033035…12379895154549994239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.922 × 10¹¹⁴(115-digit number)

19226234843517033035…12379895154549994241

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

3.845 × 10¹¹⁴(115-digit number)

38452469687034066070…24759790309099988479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.845 × 10¹¹⁴(115-digit number)

38452469687034066070…24759790309099988481

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

7.690 × 10¹¹⁴(115-digit number)

76904939374068132140…49519580618199976959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.690 × 10¹¹⁴(115-digit number)

76904939374068132140…49519580618199976961

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 499245

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 c08cc65d1d946d76248f77b7bde0a16221a79f80e6598efdf33c2a571a6810dd

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 #499,245 on Chainz ↗