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Block #81,739

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 11:16:39 PM · Difficulty 9.2706 · 6,729,410 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

499ad5cc009d6336ebb4fadcf5963cfe7ad26a99304a827aa882d6c046a32c93

View on Chainz ↗

Height

#81,739

Difficulty

9.270591

Transactions

Size

210 B

Version

Bits

0945457a

Nonce

255,122

Timestamp

7/24/2013, 11:16:39 PM

Confirmations

6,729,410

Merkle Root

a6b88d1f725ee2f3f0f94aa3debe1d8b6030d886d2402e8991c5b9f86e1f03cd

Transactions (1)

Coinbasea6b88d1f725ee2…c5b9f86e1f03cd

1 in → 1 out11.6200 XPM109 B

AYrtgdMx…SnFDNzsA

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.

2.981 × 10¹²⁰(121-digit number)

29812053652985479337…16382766078355559040

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

2.981 × 10¹²⁰(121-digit number)

29812053652985479337…16382766078355559039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.981 × 10¹²⁰(121-digit number)

29812053652985479337…16382766078355559041

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

5.962 × 10¹²⁰(121-digit number)

59624107305970958674…32765532156711118079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.962 × 10¹²⁰(121-digit number)

59624107305970958674…32765532156711118081

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

1.192 × 10¹²¹(122-digit number)

11924821461194191734…65531064313422236159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.192 × 10¹²¹(122-digit number)

11924821461194191734…65531064313422236161

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

2.384 × 10¹²¹(122-digit number)

23849642922388383469…31062128626844472319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.384 × 10¹²¹(122-digit number)

23849642922388383469…31062128626844472321

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

4.769 × 10¹²¹(122-digit number)

47699285844776766939…62124257253688944639

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 81739

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 499ad5cc009d6336ebb4fadcf5963cfe7ad26a99304a827aa882d6c046a32c93

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 #81,739 on Chainz ↗

Block #81,739

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