Home/Chain Registry/Block #81,302

Block #81,302

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 4:06:34 PM · Difficulty 9.2694 · 6,712,038 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6c494c31f661a11507a06a6dc03720ca039cf4812014bb29e0095ee75901f225

View on Chainz ↗

Height

#81,302

Difficulty

9.269404

Transactions

Size

209 B

Version

Bits

0944f7ac

Nonce

Timestamp

7/24/2013, 4:06:34 PM

Confirmations

6,712,038

Merkle Root

ac8db71e92562957a52d4eac34fcce7df7775a4c0f5ee715f61868da148b2539

Transactions (1)

Coinbaseac8db71e925629…1868da148b2539

1 in → 1 out11.6200 XPM110 B

AdmN7yjE…tywbGavN

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.

6.528 × 10¹¹⁶(117-digit number)

65287799990382025283…32890462616249578880

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

6.528 × 10¹¹⁶(117-digit number)

65287799990382025283…32890462616249578879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.528 × 10¹¹⁶(117-digit number)

65287799990382025283…32890462616249578881

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

1.305 × 10¹¹⁷(118-digit number)

13057559998076405056…65780925232499157759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.305 × 10¹¹⁷(118-digit number)

13057559998076405056…65780925232499157761

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

2.611 × 10¹¹⁷(118-digit number)

26115119996152810113…31561850464998315519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.611 × 10¹¹⁷(118-digit number)

26115119996152810113…31561850464998315521

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

5.223 × 10¹¹⁷(118-digit number)

52230239992305620226…63123700929996631039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.223 × 10¹¹⁷(118-digit number)

52230239992305620226…63123700929996631041

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

1.044 × 10¹¹⁸(119-digit number)

10446047998461124045…26247401859993262079

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 81302

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 6c494c31f661a11507a06a6dc03720ca039cf4812014bb29e0095ee75901f225

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 #81,302 on Chainz ↗