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Block #199,430

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/8/2013, 9:09:32 AM · Difficulty 9.8875 · 6,606,760 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d77d15106d6bd54846860ee5c1663e44bd0c3c93b115df75a29b95b78c4de6cd

View on Chainz ↗

Height

#199,430

Difficulty

9.887477

Transactions

Size

3.54 KB

Version

Bits

09e331ab

Nonce

1,165,001,415

Timestamp

10/8/2013, 9:09:32 AM

Confirmations

6,606,760

Merkle Root

76df59dd38c4f231f3ca1160f83da4cba61eb010ab53c709d5834f2f571640fb

Transactions (1)

Coinbase76df59dd38c4f2…834f2f571640fb

1 in → 102 out10.1700 XPM3.45 KB

AdYbWNZ4…CChS4KyF AcKcNjCB…MZipfo4V AeWxj9Kg…68s5ydDz AWVGtkZj…m321bzSA Adct132a…HMu1F3uZ

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.

7.311 × 10⁹⁷(98-digit number)

73117462969940850031…36718299292946568320

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

7.311 × 10⁹⁷(98-digit number)

73117462969940850031…36718299292946568319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.311 × 10⁹⁷(98-digit number)

73117462969940850031…36718299292946568321

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

1.462 × 10⁹⁸(99-digit number)

14623492593988170006…73436598585893136639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.462 × 10⁹⁸(99-digit number)

14623492593988170006…73436598585893136641

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

2.924 × 10⁹⁸(99-digit number)

29246985187976340012…46873197171786273279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.924 × 10⁹⁸(99-digit number)

29246985187976340012…46873197171786273281

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

5.849 × 10⁹⁸(99-digit number)

58493970375952680025…93746394343572546559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.849 × 10⁹⁸(99-digit number)

58493970375952680025…93746394343572546561

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

1.169 × 10⁹⁹(100-digit number)

11698794075190536005…87492788687145093119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.169 × 10⁹⁹(100-digit number)

11698794075190536005…87492788687145093121

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 199430

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 d77d15106d6bd54846860ee5c1663e44bd0c3c93b115df75a29b95b78c4de6cd

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 #199,430 on Chainz ↗