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Block #41,736

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 5:11:27 PM · Difficulty 8.5490 · 6,767,419 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ea7f0e9be143d9efeedf25e99f70cd8c72c81365d829635346ced7a27b99691

View on Chainz ↗

Height

#41,736

Difficulty

8.549050

Transactions

Size

198 B

Version

Bits

088c8e86

Nonce

Timestamp

7/14/2013, 5:11:27 PM

Confirmations

6,767,419

Merkle Root

5e5f60b3b12a93c52d13dbb65f88fab41a9b2eb660821813f67509fe71d48ea2

Transactions (1)

Coinbase5e5f60b3b12a93…7509fe71d48ea2

1 in → 1 out13.6600 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.

3.338 × 10⁹¹(92-digit number)

33386682870521218955…73719020750850128240

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

3.338 × 10⁹¹(92-digit number)

33386682870521218955…73719020750850128239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.338 × 10⁹¹(92-digit number)

33386682870521218955…73719020750850128241

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

6.677 × 10⁹¹(92-digit number)

66773365741042437910…47438041501700256479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.677 × 10⁹¹(92-digit number)

66773365741042437910…47438041501700256481

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

1.335 × 10⁹²(93-digit number)

13354673148208487582…94876083003400512959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.335 × 10⁹²(93-digit number)

13354673148208487582…94876083003400512961

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

2.670 × 10⁹²(93-digit number)

26709346296416975164…89752166006801025919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.670 × 10⁹²(93-digit number)

26709346296416975164…89752166006801025921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 41736

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 6ea7f0e9be143d9efeedf25e99f70cd8c72c81365d829635346ced7a27b99691

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 #41,736 on Chainz ↗

Block #41,736

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