Home/Chain Registry/Block #242,531

Block #242,531

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/3/2013, 7:13:17 PM · Difficulty 9.9601 · 6,588,571 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99d11af5a7e329c997e74bb168f0e0514496bc0d859242c9742515875207a642

View on Chainz ↗

Height

#242,531

Difficulty

9.960058

Transactions

Size

229 B

Version

Bits

09f5c65d

Nonce

49,506

Timestamp

11/3/2013, 7:13:17 PM

Confirmations

6,588,571

Merkle Root

735148c9b2a7f639e61b906cc22d8608cb6d6ae40145151d97d86697c2e50034

Transactions (1)

Coinbase735148c9b2a7f6…d86697c2e50034

1 in → 2 out10.0700 XPM137 B

AZDUEbdS…RYKMRZET AU6kq4CL…dQBLvxLp

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.

2.993 × 10⁹⁹(100-digit number)

29932320672350086811…06876235717486224640

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

2.993 × 10⁹⁹(100-digit number)

29932320672350086811…06876235717486224639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.993 × 10⁹⁹(100-digit number)

29932320672350086811…06876235717486224641

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

5.986 × 10⁹⁹(100-digit number)

59864641344700173623…13752471434972449279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.986 × 10⁹⁹(100-digit number)

59864641344700173623…13752471434972449281

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

1.197 × 10¹⁰⁰(101-digit number)

11972928268940034724…27504942869944898559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.197 × 10¹⁰⁰(101-digit number)

11972928268940034724…27504942869944898561

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

2.394 × 10¹⁰⁰(101-digit number)

23945856537880069449…55009885739889797119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.394 × 10¹⁰⁰(101-digit number)

23945856537880069449…55009885739889797121

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

4.789 × 10¹⁰⁰(101-digit number)

47891713075760138898…10019771479779594239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.789 × 10¹⁰⁰(101-digit number)

47891713075760138898…10019771479779594241

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 242531

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 99d11af5a7e329c997e74bb168f0e0514496bc0d859242c9742515875207a642

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 #242,531 on Chainz ↗

Block #242,531

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