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Block #442,240

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2014, 4:53:35 PM · Difficulty 10.3499 · 6,370,059 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c212fda89a3d2a99711cc4968dd170d7dab8220852915d7a56b1bf7e283ce7ad

View on Chainz ↗

Height

#442,240

Difficulty

10.349868

Transactions

Size

934 B

Version

Bits

0a5990f3

Nonce

20,714

Timestamp

3/13/2014, 4:53:35 PM

Confirmations

6,370,059

Merkle Root

6087ec5538cf86128d1238a5f0ff5f3d7a736c4a33cfdfd147058dafa70bab31

Transactions (1)

Coinbase6087ec5538cf86…058dafa70bab31

1 in → 23 out9.3200 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

1.771 × 10⁹³(94-digit number)

17712467126804744216…74095129970711372400

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

1.771 × 10⁹³(94-digit number)

17712467126804744216…74095129970711372399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.771 × 10⁹³(94-digit number)

17712467126804744216…74095129970711372401

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

3.542 × 10⁹³(94-digit number)

35424934253609488433…48190259941422744799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.542 × 10⁹³(94-digit number)

35424934253609488433…48190259941422744801

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

7.084 × 10⁹³(94-digit number)

70849868507218976867…96380519882845489599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.084 × 10⁹³(94-digit number)

70849868507218976867…96380519882845489601

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

1.416 × 10⁹⁴(95-digit number)

14169973701443795373…92761039765690979199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.416 × 10⁹⁴(95-digit number)

14169973701443795373…92761039765690979201

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

2.833 × 10⁹⁴(95-digit number)

28339947402887590746…85522079531381958399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.833 × 10⁹⁴(95-digit number)

28339947402887590746…85522079531381958401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 442240

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 c212fda89a3d2a99711cc4968dd170d7dab8220852915d7a56b1bf7e283ce7ad

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 #442,240 on Chainz ↗

Block #442,240

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