Home/Chain Registry/Block #81,255

Block #81,255

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 3:32:43 PM · Difficulty 9.2675 · 6,711,413 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

01686bf556c55c2561d09c4de7ffaef692534bbf21a938bc70efb775bbf0c0e3

View on Chainz ↗

Height

#81,255

Difficulty

9.267476

Transactions

Size

199 B

Version

Bits

09447950

Nonce

44,732

Timestamp

7/24/2013, 3:32:43 PM

Confirmations

6,711,413

Merkle Root

eabc16fbcd82f1806715a14b90c31e1a7b268163a1ccd26b638cc9de063f48c2

Transactions (1)

Coinbaseeabc16fbcd82f1…8cc9de063f48c2

1 in → 1 out11.6300 XPM109 B

AN1pintt…eqoXNyFs

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.

2.857 × 10⁹⁵(96-digit number)

28572657864969022001…79915800368513027270

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

2.857 × 10⁹⁵(96-digit number)

28572657864969022001…79915800368513027269

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.857 × 10⁹⁵(96-digit number)

28572657864969022001…79915800368513027271

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

5.714 × 10⁹⁵(96-digit number)

57145315729938044002…59831600737026054539

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.714 × 10⁹⁵(96-digit number)

57145315729938044002…59831600737026054541

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

1.142 × 10⁹⁶(97-digit number)

11429063145987608800…19663201474052109079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.142 × 10⁹⁶(97-digit number)

11429063145987608800…19663201474052109081

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

2.285 × 10⁹⁶(97-digit number)

22858126291975217601…39326402948104218159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.285 × 10⁹⁶(97-digit number)

22858126291975217601…39326402948104218161

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

4.571 × 10⁹⁶(97-digit number)

45716252583950435202…78652805896208436319

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 81255

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 01686bf556c55c2561d09c4de7ffaef692534bbf21a938bc70efb775bbf0c0e3

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 #81,255 on Chainz ↗