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Block #264,606

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/18/2013, 8:32:42 PM · Difficulty 9.9640 · 6,534,233 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3861f6913b7a67b3cb3e4e2975b82dfe8b8e21c274c7df71b8e545861ad27294

View on Chainz ↗

Height

#264,606

Difficulty

9.964024

Transactions

Size

602 B

Version

Bits

09f6ca48

Nonce

16,930

Timestamp

11/18/2013, 8:32:42 PM

Confirmations

6,534,233

Merkle Root

918c8518656b1d585a5d036b1b26bca95bd1f2aff67ff8d4e8b02f399945574a

Transactions (2)

Coinbased6372cf450e7d4…cc34b7b7985a7b

1 in → 2 out10.0700 XPM137 B

AKcbk49N…GJbKa7j1 AKNbfPoc…jfkpwAyL

945c4d108e80eb…bd821e7fb7258d

2 in → 2 out1.1300 XPM374 B

AS4CBeic…dxyNFsDK AH1yGJS9…AgHPYXwT

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.

1.326 × 10⁹⁷(98-digit number)

13268417527266700469…38689370128585671680

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

1.326 × 10⁹⁷(98-digit number)

13268417527266700469…38689370128585671679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.326 × 10⁹⁷(98-digit number)

13268417527266700469…38689370128585671681

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

2.653 × 10⁹⁷(98-digit number)

26536835054533400939…77378740257171343359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.653 × 10⁹⁷(98-digit number)

26536835054533400939…77378740257171343361

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

5.307 × 10⁹⁷(98-digit number)

53073670109066801878…54757480514342686719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.307 × 10⁹⁷(98-digit number)

53073670109066801878…54757480514342686721

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

1.061 × 10⁹⁸(99-digit number)

10614734021813360375…09514961028685373439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.061 × 10⁹⁸(99-digit number)

10614734021813360375…09514961028685373441

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

2.122 × 10⁹⁸(99-digit number)

21229468043626720751…19029922057370746879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.122 × 10⁹⁸(99-digit number)

21229468043626720751…19029922057370746881

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 264606

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 3861f6913b7a67b3cb3e4e2975b82dfe8b8e21c274c7df71b8e545861ad27294

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 #264,606 on Chainz ↗