Home/Chain Registry/Block #283,210

Block #283,210

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 3:59:48 PM · Difficulty 9.9807 · 6,515,685 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43a870445e61d66e8becb6acd4e50c851e2f7b0ca5b55dfdbbc62b28e3c2fdb2

View on Chainz ↗

Height

#283,210

Difficulty

9.980676

Transactions

Size

1.15 KB

Version

Bits

09fb0d94

Nonce

292,398

Timestamp

11/29/2013, 3:59:48 PM

Confirmations

6,515,685

Merkle Root

fdbe0d1504d792f67934c6d088ea997e880f956f6d108f8c831011ae91471cc8

Transactions (1)

Coinbasefdbe0d1504d792…1011ae91471cc8

1 in → 30 out10.0000 XPM1.06 KB

AGFAJ5YL…ZEnBbk6G AQwRN8bE…V8PsTcY9 AKde1i4d…88R1bw6g AbtgNzNb…9Atvu81w Ad9pSzHt…cpJ3y2zz

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.

3.060 × 10⁹³(94-digit number)

30608605833764795039…33495761526005741440

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

3.060 × 10⁹³(94-digit number)

30608605833764795039…33495761526005741439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.060 × 10⁹³(94-digit number)

30608605833764795039…33495761526005741441

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

6.121 × 10⁹³(94-digit number)

61217211667529590079…66991523052011482879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.121 × 10⁹³(94-digit number)

61217211667529590079…66991523052011482881

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

1.224 × 10⁹⁴(95-digit number)

12243442333505918015…33983046104022965759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.224 × 10⁹⁴(95-digit number)

12243442333505918015…33983046104022965761

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

2.448 × 10⁹⁴(95-digit number)

24486884667011836031…67966092208045931519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.448 × 10⁹⁴(95-digit number)

24486884667011836031…67966092208045931521

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

4.897 × 10⁹⁴(95-digit number)

48973769334023672063…35932184416091863039

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 283210

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 43a870445e61d66e8becb6acd4e50c851e2f7b0ca5b55dfdbbc62b28e3c2fdb2

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 #283,210 on Chainz ↗