Home/Chain Registry/Block #221,966

Block #221,966

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 9:30:56 PM · Difficulty 9.9399 · 6,569,421 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f4c4bb35ec3ff2986413a6fac287318e310b4cb70880d28e2d3de4b83701051e

View on Chainz ↗

Height

#221,966

Difficulty

9.939851

Transactions

Size

206 B

Version

Bits

09f09a17

Nonce

379,402

Timestamp

10/21/2013, 9:30:56 PM

Confirmations

6,569,421

Merkle Root

69eb675c5b475f42c280fb1d8f5e90611e55d729cc5a9c8877166b2821b9c3b5

Transactions (1)

Coinbase69eb675c5b475f…166b2821b9c3b5

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.

1.136 × 10⁹⁴(95-digit number)

11367711250941263916…18441397374297272320

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

1.136 × 10⁹⁴(95-digit number)

11367711250941263916…18441397374297272319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.136 × 10⁹⁴(95-digit number)

11367711250941263916…18441397374297272321

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

2.273 × 10⁹⁴(95-digit number)

22735422501882527833…36882794748594544639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.273 × 10⁹⁴(95-digit number)

22735422501882527833…36882794748594544641

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

4.547 × 10⁹⁴(95-digit number)

45470845003765055667…73765589497189089279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.547 × 10⁹⁴(95-digit number)

45470845003765055667…73765589497189089281

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

9.094 × 10⁹⁴(95-digit number)

90941690007530111334…47531178994378178559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.094 × 10⁹⁴(95-digit number)

90941690007530111334…47531178994378178561

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

1.818 × 10⁹⁵(96-digit number)

18188338001506022266…95062357988756357119

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 221966

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 f4c4bb35ec3ff2986413a6fac287318e310b4cb70880d28e2d3de4b83701051e

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 #221,966 on Chainz ↗