Home/Chain Registry/Block #258,819

Block #258,819

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/13/2013, 6:36:23 AM · Difficulty 9.9767 · 6,537,166 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6a93e07a12312b2144ed5cdb570248aebbc127ef72e1ed2f11cb1ebe2357c729

View on Chainz ↗

Height

#258,819

Difficulty

9.976739

Transactions

Size

1.97 KB

Version

Bits

09fa0b97

Nonce

145,776

Timestamp

11/13/2013, 6:36:23 AM

Confirmations

6,537,166

Merkle Root

9a67880f555ce191a4a7fc9b28ff2858b082d132ed3bb05056587b6bf5b6f55e

Transactions (1)

Coinbase9a67880f555ce1…587b6bf5b6f55e

1 in → 55 out10.0100 XPM1.89 KB

AZ2pPuKg…95SN2Yr7 Ab2f51dk…irxE26FW AQtzUSwq…htAuF3yC AHeVugNM…1STQZ4jA APZy8y6E…QZaGQjfp

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.

2.727 × 10⁹¹(92-digit number)

27279632993958622637…66034938545522357280

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

2.727 × 10⁹¹(92-digit number)

27279632993958622637…66034938545522357279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.727 × 10⁹¹(92-digit number)

27279632993958622637…66034938545522357281

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

5.455 × 10⁹¹(92-digit number)

54559265987917245275…32069877091044714559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.455 × 10⁹¹(92-digit number)

54559265987917245275…32069877091044714561

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

1.091 × 10⁹²(93-digit number)

10911853197583449055…64139754182089429119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.091 × 10⁹²(93-digit number)

10911853197583449055…64139754182089429121

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

2.182 × 10⁹²(93-digit number)

21823706395166898110…28279508364178858239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.182 × 10⁹²(93-digit number)

21823706395166898110…28279508364178858241

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

4.364 × 10⁹²(93-digit number)

43647412790333796220…56559016728357716479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 258819

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 6a93e07a12312b2144ed5cdb570248aebbc127ef72e1ed2f11cb1ebe2357c729

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 #258,819 on Chainz ↗