Home/Chain Registry/Block #41,491

Block #41,491

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 4:44:53 PM · Difficulty 8.5290 · 6,747,997 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

17bcdd15de0b4295be5d9ee27d7c903209fec508b636c6271b792a6ec5ce38df

View on Chainz ↗

Height

#41,491

Difficulty

8.528997

Transactions

Size

358 B

Version

Bits

08876c5a

Nonce

619

Timestamp

7/14/2013, 4:44:53 PM

Confirmations

6,747,997

Merkle Root

4ad4311d30ffaf61fa4c335bcfb60fada27c21f2c59620e6460d1a2bbbe45df9

Transactions (2)

Coinbaseafb27f9db74877…7670ecfa75cfcf

1 in → 1 out13.7400 XPM110 B

AeKmzxNA…MZ4kLPxd

ba22708d949794…46eca7632ef359

1 in → 1 out14.9900 XPM159 B

AXUtFnVB…2K4kmJnq

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.

1.884 × 10⁹³(94-digit number)

18843013386551014069…47204609759082390860

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

1.884 × 10⁹³(94-digit number)

18843013386551014069…47204609759082390859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.884 × 10⁹³(94-digit number)

18843013386551014069…47204609759082390861

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

3.768 × 10⁹³(94-digit number)

37686026773102028139…94409219518164781719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.768 × 10⁹³(94-digit number)

37686026773102028139…94409219518164781721

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

7.537 × 10⁹³(94-digit number)

75372053546204056278…88818439036329563439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.537 × 10⁹³(94-digit number)

75372053546204056278…88818439036329563441

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

1.507 × 10⁹⁴(95-digit number)

15074410709240811255…77636878072659126879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.507 × 10⁹⁴(95-digit number)

15074410709240811255…77636878072659126881

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 41491

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 17bcdd15de0b4295be5d9ee27d7c903209fec508b636c6271b792a6ec5ce38df

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 #41,491 on Chainz ↗