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Block #188,180

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/1/2013, 12:53:31 AM · Difficulty 9.8697 · 6,623,656 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a4540adfa24c5b442299f920e926499aa8ef012aa0e182e2e7bb2b20ea56577a

View on Chainz ↗

Height

#188,180

Difficulty

9.869671

Transactions

Size

798 B

Version

Bits

09dea2be

Nonce

3,766

Timestamp

10/1/2013, 12:53:31 AM

Confirmations

6,623,656

Merkle Root

681568b73a746d834b52e6fa32d279f72d399a9597cbfdd04e5a8d95a52e5e07

Transactions (3)

Coinbasec9c41ffafb9717…24257688b36f1a

1 in → 1 out10.2700 XPM109 B

AHxswfvc…28HYLkw7

c7b1c5580ac79e…92bd3a6f004233

1 in → 2 out10.2600 XPM225 B

APXvLgCU…cA56aaxC AH3dDrPX…iXBYe8ZV

de49d7bfd10760…0d80ce4c633175

2 in → 2 out10.3438 XPM374 B

ALpthvGg…D1g5z4CT Ab2Hppxu…pNgPkL5B

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.

8.127 × 10⁹³(94-digit number)

81279206514545182151…64981735933578347840

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

8.127 × 10⁹³(94-digit number)

81279206514545182151…64981735933578347839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.127 × 10⁹³(94-digit number)

81279206514545182151…64981735933578347841

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

1.625 × 10⁹⁴(95-digit number)

16255841302909036430…29963471867156695679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.625 × 10⁹⁴(95-digit number)

16255841302909036430…29963471867156695681

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

3.251 × 10⁹⁴(95-digit number)

32511682605818072860…59926943734313391359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.251 × 10⁹⁴(95-digit number)

32511682605818072860…59926943734313391361

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

6.502 × 10⁹⁴(95-digit number)

65023365211636145721…19853887468626782719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.502 × 10⁹⁴(95-digit number)

65023365211636145721…19853887468626782721

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

1.300 × 10⁹⁵(96-digit number)

13004673042327229144…39707774937253565439

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 188180

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 a4540adfa24c5b442299f920e926499aa8ef012aa0e182e2e7bb2b20ea56577a

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 #188,180 on Chainz ↗

Block #188,180

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