Home/Chain Registry/Block #343,214

Block #343,214

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/4/2014, 1:30:10 PM · Difficulty 10.1710 · 6,482,975 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f69bc43a6d789328d5563b19d5fa81db7d12b3e256ce6e390ae1f5687446022

View on Chainz ↗

Height

#343,214

Difficulty

10.170970

Transactions

Size

575 B

Version

Bits

0a2bc4ac

Nonce

18,299

Timestamp

1/4/2014, 1:30:10 PM

Confirmations

6,482,975

Merkle Root

3fd8b24947d50a7b0220a0a39421b1df84f66c7099b92fb1ea12689a0dea2864

Transactions (2)

Coinbase7cae77b6349fb2…aaf15181383bb9

1 in → 1 out9.6600 XPM110 B

AeKNrjNj…1NEq95Ta

d385725edc4ca9…747f72c11822e2

2 in → 2 out1.0102 XPM373 B

AFpfQwU3…rChsvy6H AcfNEgxY…DMyXWp7J

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.

6.064 × 10⁹⁹(100-digit number)

60641695857162426209…70103418624544515280

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

6.064 × 10⁹⁹(100-digit number)

60641695857162426209…70103418624544515279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.064 × 10⁹⁹(100-digit number)

60641695857162426209…70103418624544515281

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

1.212 × 10¹⁰⁰(101-digit number)

12128339171432485241…40206837249089030559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.212 × 10¹⁰⁰(101-digit number)

12128339171432485241…40206837249089030561

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

2.425 × 10¹⁰⁰(101-digit number)

24256678342864970483…80413674498178061119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.425 × 10¹⁰⁰(101-digit number)

24256678342864970483…80413674498178061121

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

4.851 × 10¹⁰⁰(101-digit number)

48513356685729940967…60827348996356122239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.851 × 10¹⁰⁰(101-digit number)

48513356685729940967…60827348996356122241

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

9.702 × 10¹⁰⁰(101-digit number)

97026713371459881934…21654697992712244479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.702 × 10¹⁰⁰(101-digit number)

97026713371459881934…21654697992712244481

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 343214

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 3f69bc43a6d789328d5563b19d5fa81db7d12b3e256ce6e390ae1f5687446022

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 #343,214 on Chainz ↗

Block #343,214

Cookie Preferences