Home/Chain Registry/Block #279,735

Block #279,735

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 10:54:44 AM · Difficulty 9.9726 · 6,520,727 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

624a4856de19dfb26e97cce8107cb7fb5f6ef65118255c49db0cffe69d786363

View on Chainz ↗

Height

#279,735

Difficulty

9.972626

Transactions

Size

21.03 KB

Version

Bits

09f8fe04

Nonce

21,434

Timestamp

11/28/2013, 10:54:44 AM

Confirmations

6,520,727

Merkle Root

dbf0c9d8820bb9f1e478416313c5a2ad604659bb464c175684d83ee0565373ec

Transactions (4)

Coinbased54eb36994cc5d…c72c8f2bec454c

1 in → 30 out10.0200 XPM1.06 KB

AScAzqGc…BZ6tV1vJ AWA5FEzr…x9RdPKTy AZ2pPuKg…95SN2Yr7 ALw8WzMm…sj2uYfgL AbtgNzNb…9Atvu81w

8de8e5417368f9…b4eefa7cdada85

11 in → 2 out94.5000 XPM1.67 KB

ANB4VHgQ…fnrVqUMG AYekPV1w…TjT1ZZK7

46fe3b0e6340d1…f01b42984c3502

4 in → 2 out403.2448 XPM672 B

AKdj28LG…TPk4uLyt ANPHK5yX…diwNf4Lg

2e38c9bdd8ba3f…1d955aa2643639

123 in → 2 out135.0101 XPM17.56 KB

AR24vtgA…DNdtqa6z AZY1kcTm…mV2wWE3E

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.

1.866 × 10⁹⁵(96-digit number)

18664739268923638215…06573697213581141360

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

1.866 × 10⁹⁵(96-digit number)

18664739268923638215…06573697213581141359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.866 × 10⁹⁵(96-digit number)

18664739268923638215…06573697213581141361

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

3.732 × 10⁹⁵(96-digit number)

37329478537847276431…13147394427162282719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.732 × 10⁹⁵(96-digit number)

37329478537847276431…13147394427162282721

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

7.465 × 10⁹⁵(96-digit number)

74658957075694552863…26294788854324565439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.465 × 10⁹⁵(96-digit number)

74658957075694552863…26294788854324565441

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

1.493 × 10⁹⁶(97-digit number)

14931791415138910572…52589577708649130879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.493 × 10⁹⁶(97-digit number)

14931791415138910572…52589577708649130881

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

2.986 × 10⁹⁶(97-digit number)

29863582830277821145…05179155417298261759

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 279735

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 624a4856de19dfb26e97cce8107cb7fb5f6ef65118255c49db0cffe69d786363

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 #279,735 on Chainz ↗