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Block #234,302

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/30/2013, 6:06:18 AM · Difficulty 9.9438 · 6,558,366 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9e7bcf6b44f755f1dd57aac3c245d7f2e03ede34b4f4d7729f31d4696fdfa336

View on Chainz ↗

Height

#234,302

Difficulty

9.943834

Transactions

Size

199 B

Version

Bits

09f19f1b

Nonce

195,648

Timestamp

10/30/2013, 6:06:18 AM

Confirmations

6,558,366

Merkle Root

28fcf69253f6243669f885c3d1143e91fa42b9598d91345761fad03d951ea48d

Transactions (1)

Coinbase28fcf69253f624…fad03d951ea48d

1 in → 1 out10.1000 XPM109 B

AYZUGpXa…W7UKsvcT

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.

3.032 × 10⁹⁵(96-digit number)

30322136059235997503…84279811758088035920

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

3.032 × 10⁹⁵(96-digit number)

30322136059235997503…84279811758088035919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.032 × 10⁹⁵(96-digit number)

30322136059235997503…84279811758088035921

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

6.064 × 10⁹⁵(96-digit number)

60644272118471995006…68559623516176071839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.064 × 10⁹⁵(96-digit number)

60644272118471995006…68559623516176071841

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

1.212 × 10⁹⁶(97-digit number)

12128854423694399001…37119247032352143679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.212 × 10⁹⁶(97-digit number)

12128854423694399001…37119247032352143681

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

2.425 × 10⁹⁶(97-digit number)

24257708847388798002…74238494064704287359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.425 × 10⁹⁶(97-digit number)

24257708847388798002…74238494064704287361

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

4.851 × 10⁹⁶(97-digit number)

48515417694777596005…48476988129408574719

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 234302

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 9e7bcf6b44f755f1dd57aac3c245d7f2e03ede34b4f4d7729f31d4696fdfa336

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 #234,302 on Chainz ↗