Home/Chain Registry/Block #94,195

Block #94,195

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/2/2013, 10:33:37 PM · Difficulty 9.2017 · 6,697,399 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8b743b57da68d3ae667c5ce3b267c88223b481c4170b12c3b876e5b6faf293ce

View on Chainz ↗

Height

#94,195

Difficulty

9.201693

Transactions

Size

205 B

Version

Bits

0933a22c

Nonce

114,331

Timestamp

8/2/2013, 10:33:37 PM

Confirmations

6,697,399

Merkle Root

2c57caec9ed0abc0cef9c5e78823f2a5dcde569924184544ffea2cf35de2875e

Transactions (1)

Coinbase2c57caec9ed0ab…ea2cf35de2875e

1 in → 1 out11.7900 XPM109 B

AK1JUKWL…oPR4rN5o

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.

7.994 × 10¹⁰⁷(108-digit number)

79945686871271677773…44714716326189116630

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

7.994 × 10¹⁰⁷(108-digit number)

79945686871271677773…44714716326189116629

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.994 × 10¹⁰⁷(108-digit number)

79945686871271677773…44714716326189116631

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

1.598 × 10¹⁰⁸(109-digit number)

15989137374254335554…89429432652378233259

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.598 × 10¹⁰⁸(109-digit number)

15989137374254335554…89429432652378233261

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

3.197 × 10¹⁰⁸(109-digit number)

31978274748508671109…78858865304756466519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.197 × 10¹⁰⁸(109-digit number)

31978274748508671109…78858865304756466521

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

6.395 × 10¹⁰⁸(109-digit number)

63956549497017342219…57717730609512933039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.395 × 10¹⁰⁸(109-digit number)

63956549497017342219…57717730609512933041

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

1.279 × 10¹⁰⁹(110-digit number)

12791309899403468443…15435461219025866079

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 94195

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 8b743b57da68d3ae667c5ce3b267c88223b481c4170b12c3b876e5b6faf293ce

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 #94,195 on Chainz ↗