Home/Chain Registry/Block #7,544

Block #7,544

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/10/2013, 10:22:14 AM · Difficulty 7.5218 · 6,802,130 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b44901ac7e4f9af0a80c1babf5ac8a9bb40a30c444032a26cd88ae88c9591eb4

View on Chainz ↗

Height

#7,544

Difficulty

7.521825

Transactions

Size

199 B

Version

Bits

0785964c

Nonce

628

Timestamp

7/10/2013, 10:22:14 AM

Confirmations

6,802,130

Merkle Root

123afb1889a92d38d84ead2ed9d30bf3961773c49c5c39841e5ee10e9d742326

Transactions (1)

Coinbase123afb1889a92d…5ee10e9d742326

1 in → 1 out17.6500 XPM109 B

AJUX2nVz…aBC7pP7u

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.

4.626 × 10⁹⁴(95-digit number)

46268551392862619798…46028722671042150400

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

4.626 × 10⁹⁴(95-digit number)

46268551392862619798…46028722671042150399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.626 × 10⁹⁴(95-digit number)

46268551392862619798…46028722671042150401

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

9.253 × 10⁹⁴(95-digit number)

92537102785725239597…92057445342084300799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.253 × 10⁹⁴(95-digit number)

92537102785725239597…92057445342084300801

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

1.850 × 10⁹⁵(96-digit number)

18507420557145047919…84114890684168601599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.850 × 10⁹⁵(96-digit number)

18507420557145047919…84114890684168601601

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

3.701 × 10⁹⁵(96-digit number)

37014841114290095838…68229781368337203199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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 7544

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 b44901ac7e4f9af0a80c1babf5ac8a9bb40a30c444032a26cd88ae88c9591eb4

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 #7,544 on Chainz ↗

Block #7,544

Cookie Preferences