Home/Chain Registry/Block #1,850,279

Block #1,850,279

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/15/2016, 3:00:00 PM · Difficulty 10.6290 · 4,989,294 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

616c91f7db5b67d7a24ca5dcda2f5474947ef37dd9b077eb1ebc774b0d7c219e

View on Chainz ↗

Height

#1,850,279

Difficulty

10.628957

Transactions

Size

3.74 KB

Version

Bits

0aa10352

Nonce

753,375,984

Timestamp

11/15/2016, 3:00:00 PM

Confirmations

4,989,294

Merkle Root

5147f469e21675d562d35b721fb3192cc5aa838586cfa67ba63f0521c63bda77

Transactions (2)

Coinbase381e77e855417f…73913e0feb6e4e

1 in → 1 out8.8800 XPM110 B

ASDbVqas…QqKnwJov

337fb4a81264a3…ece3c4fbc43862

24 in → 2 out84.2932 XPM3.54 KB

AcvkebbA…zfaPCZDq AMx8Esnt…97T9RVgd

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.

3.267 × 10⁹⁴(95-digit number)

32677282864587547796…30091648870494989240

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

3.267 × 10⁹⁴(95-digit number)

32677282864587547796…30091648870494989239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.267 × 10⁹⁴(95-digit number)

32677282864587547796…30091648870494989241

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

6.535 × 10⁹⁴(95-digit number)

65354565729175095593…60183297740989978479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.535 × 10⁹⁴(95-digit number)

65354565729175095593…60183297740989978481

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

1.307 × 10⁹⁵(96-digit number)

13070913145835019118…20366595481979956959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.307 × 10⁹⁵(96-digit number)

13070913145835019118…20366595481979956961

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

2.614 × 10⁹⁵(96-digit number)

26141826291670038237…40733190963959913919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.614 × 10⁹⁵(96-digit number)

26141826291670038237…40733190963959913921

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

5.228 × 10⁹⁵(96-digit number)

52283652583340076475…81466381927919827839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.228 × 10⁹⁵(96-digit number)

52283652583340076475…81466381927919827841

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 1850279

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 616c91f7db5b67d7a24ca5dcda2f5474947ef37dd9b077eb1ebc774b0d7c219e

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 #1,850,279 on Chainz ↗

Block #1,850,279

Cookie Preferences