Home/Chain Registry/Block #144,225

Block #144,225

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/1/2013, 4:33:19 AM · Difficulty 9.8383 · 6,645,597 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ad8fadd79dba72a1715fd95a29a4b4816721d242c3ef282e2d6695a3ef7dbab6

View on Chainz ↗

Height

#144,225

Difficulty

9.838262

Transactions

Size

200 B

Version

Bits

09d6985f

Nonce

69,430

Timestamp

9/1/2013, 4:33:19 AM

Confirmations

6,645,597

Merkle Root

2eaf63367346646bee4c5d6536868a538397c28f0c559bdc15f74aca0834ce53

Transactions (1)

Coinbase2eaf6336734664…f74aca0834ce53

1 in → 1 out10.3200 XPM109 B

ALcG2AET…ZZrjqk1i

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.

1.144 × 10⁹⁶(97-digit number)

11447221107850805983…81040629009471693120

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

1.144 × 10⁹⁶(97-digit number)

11447221107850805983…81040629009471693119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.144 × 10⁹⁶(97-digit number)

11447221107850805983…81040629009471693121

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

2.289 × 10⁹⁶(97-digit number)

22894442215701611967…62081258018943386239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.289 × 10⁹⁶(97-digit number)

22894442215701611967…62081258018943386241

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

4.578 × 10⁹⁶(97-digit number)

45788884431403223934…24162516037886772479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.578 × 10⁹⁶(97-digit number)

45788884431403223934…24162516037886772481

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

9.157 × 10⁹⁶(97-digit number)

91577768862806447868…48325032075773544959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.157 × 10⁹⁶(97-digit number)

91577768862806447868…48325032075773544961

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

1.831 × 10⁹⁷(98-digit number)

18315553772561289573…96650064151547089919

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 144225

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 ad8fadd79dba72a1715fd95a29a4b4816721d242c3ef282e2d6695a3ef7dbab6

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 #144,225 on Chainz ↗