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Block #222,936

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/22/2013, 2:36:34 PM · Difficulty 9.9392 · 6,569,833 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a367e9211cbb31eeb05c2a5cad44b2d355f4540c29a4b6798ca834e624a19f33

View on Chainz ↗

Height

#222,936

Difficulty

9.939244

Transactions

Size

205 B

Version

Bits

09f0724f

Nonce

218,329

Timestamp

10/22/2013, 2:36:34 PM

Confirmations

6,569,833

Merkle Root

de2d66d411d416d3273c874387a653f505092cce8b74078a8dbae481980c600c

Transactions (1)

Coinbasede2d66d411d416…bae481980c600c

1 in → 1 out10.1100 XPM116 B

AcLBm5Z9…S683d7c3

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.

5.811 × 10⁹¹(92-digit number)

58111375028104452077…10933226042124237920

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

5.811 × 10⁹¹(92-digit number)

58111375028104452077…10933226042124237919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.811 × 10⁹¹(92-digit number)

58111375028104452077…10933226042124237921

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

1.162 × 10⁹²(93-digit number)

11622275005620890415…21866452084248475839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.162 × 10⁹²(93-digit number)

11622275005620890415…21866452084248475841

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

2.324 × 10⁹²(93-digit number)

23244550011241780830…43732904168496951679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.324 × 10⁹²(93-digit number)

23244550011241780830…43732904168496951681

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

4.648 × 10⁹²(93-digit number)

46489100022483561661…87465808336993903359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.648 × 10⁹²(93-digit number)

46489100022483561661…87465808336993903361

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

9.297 × 10⁹²(93-digit number)

92978200044967123323…74931616673987806719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.297 × 10⁹²(93-digit number)

92978200044967123323…74931616673987806721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.859 × 10⁹³(94-digit number)

18595640008993424664…49863233347975613439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 222936

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 a367e9211cbb31eeb05c2a5cad44b2d355f4540c29a4b6798ca834e624a19f33

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 #222,936 on Chainz ↗