Home/Chain Registry/Block #238,223

Block #238,223

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/1/2013, 11:09:17 AM · Difficulty 9.9516 · 6,564,247 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

423e6f7fbcc27894f33464ebcb499c04b8ac5742a1978c570670b845162d8d04

View on Chainz ↗

Height

#238,223

Difficulty

9.951627

Transactions

Size

615 B

Version

Bits

09f39dcf

Nonce

235,198

Timestamp

11/1/2013, 11:09:17 AM

Confirmations

6,564,247

Merkle Root

6dfeb2ee8cbcc8e9033925e18593ea7c41f35ef2ad437c299692a1b7936292fd

Transactions (3)

Coinbased07bb93ae01ed5…6ab81cc4aada69

1 in → 1 out10.1000 XPM109 B

AK9vVy2j…niNoc5U8

648086196130eb…809b77feed1465

1 in → 2 out10.0900 XPM191 B

AQsUGPHm…Gg9gQvCy ARRVAhEN…FV41UNe4

73ddf8bab8da55…80df92ec53b566

1 in → 2 out4.1564 XPM226 B

AGyhc9Ym…YqF23X8n ARKHrqfD…B59wxmdc

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.

2.557 × 10⁹³(94-digit number)

25570988837461012516…08608083637758975650

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

2.557 × 10⁹³(94-digit number)

25570988837461012516…08608083637758975649

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.557 × 10⁹³(94-digit number)

25570988837461012516…08608083637758975651

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

5.114 × 10⁹³(94-digit number)

51141977674922025032…17216167275517951299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.114 × 10⁹³(94-digit number)

51141977674922025032…17216167275517951301

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

1.022 × 10⁹⁴(95-digit number)

10228395534984405006…34432334551035902599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.022 × 10⁹⁴(95-digit number)

10228395534984405006…34432334551035902601

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

2.045 × 10⁹⁴(95-digit number)

20456791069968810013…68864669102071805199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.045 × 10⁹⁴(95-digit number)

20456791069968810013…68864669102071805201

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

4.091 × 10⁹⁴(95-digit number)

40913582139937620026…37729338204143610399

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 238223

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 423e6f7fbcc27894f33464ebcb499c04b8ac5742a1978c570670b845162d8d04

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 #238,223 on Chainz ↗