Home/Chain Registry/Block #86,082

Block #86,082

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 9:33:08 PM · Difficulty 9.2890 · 6,703,782 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

23947365ee5329503adfa535df13488f450345e5088e13381600c5daa1cab04e

View on Chainz ↗

Height

#86,082

Difficulty

9.288954

Transactions

Size

199 B

Version

Bits

0949f8e7

Nonce

781

Timestamp

7/27/2013, 9:33:08 PM

Confirmations

6,703,782

Merkle Root

e1a8bb22425baa9ae5d3ce16f9e1abeebf12030450a6c304bbc24a30a14c05c7

Transactions (1)

Coinbasee1a8bb22425baa…c24a30a14c05c7

1 in → 1 out11.5700 XPM110 B

AegQAVJq…yPQ4X77i

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.

6.329 × 10⁹¹(92-digit number)

63297954023049330265…13116180252109330240

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

6.329 × 10⁹¹(92-digit number)

63297954023049330265…13116180252109330239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.329 × 10⁹¹(92-digit number)

63297954023049330265…13116180252109330241

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

1.265 × 10⁹²(93-digit number)

12659590804609866053…26232360504218660479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.265 × 10⁹²(93-digit number)

12659590804609866053…26232360504218660481

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

2.531 × 10⁹²(93-digit number)

25319181609219732106…52464721008437320959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.531 × 10⁹²(93-digit number)

25319181609219732106…52464721008437320961

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

5.063 × 10⁹²(93-digit number)

50638363218439464212…04929442016874641919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.063 × 10⁹²(93-digit number)

50638363218439464212…04929442016874641921

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

1.012 × 10⁹³(94-digit number)

10127672643687892842…09858884033749283839

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 86082

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 23947365ee5329503adfa535df13488f450345e5088e13381600c5daa1cab04e

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 #86,082 on Chainz ↗