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Block #373,321

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/24/2014, 5:44:39 AM · Difficulty 10.4254 · 6,452,144 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2aee3bcdfbbb83bfd2a95aaf162fc9457f3518b85571560f7a2b73a1023c222f

View on Chainz ↗

Height

#373,321

Difficulty

10.425406

Transactions

Size

209 B

Version

Bits

0a6ce76d

Nonce

23,690

Timestamp

1/24/2014, 5:44:39 AM

Confirmations

6,452,144

Merkle Root

b533bb4639500a9ce61bef3f229aeb542431d9657f58477496716b6986eb7bb8

Transactions (1)

Coinbaseb533bb4639500a…716b6986eb7bb8

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

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.

8.141 × 10¹⁰⁰(101-digit number)

81413593065518214252…95554254320771319040

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

8.141 × 10¹⁰⁰(101-digit number)

81413593065518214252…95554254320771319039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.141 × 10¹⁰⁰(101-digit number)

81413593065518214252…95554254320771319041

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

1.628 × 10¹⁰¹(102-digit number)

16282718613103642850…91108508641542638079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.628 × 10¹⁰¹(102-digit number)

16282718613103642850…91108508641542638081

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

3.256 × 10¹⁰¹(102-digit number)

32565437226207285700…82217017283085276159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.256 × 10¹⁰¹(102-digit number)

32565437226207285700…82217017283085276161

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

6.513 × 10¹⁰¹(102-digit number)

65130874452414571401…64434034566170552319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.513 × 10¹⁰¹(102-digit number)

65130874452414571401…64434034566170552321

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

1.302 × 10¹⁰²(103-digit number)

13026174890482914280…28868069132341104639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.302 × 10¹⁰²(103-digit number)

13026174890482914280…28868069132341104641

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 373321

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 2aee3bcdfbbb83bfd2a95aaf162fc9457f3518b85571560f7a2b73a1023c222f

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 #373,321 on Chainz ↗

Block #373,321

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