Home/Chain Registry/Block #243,509

Block #243,509

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 8:21:47 AM · Difficulty 9.9616 · 6,599,329 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e8b371cf827bbbbdefd0466c5b4c051324f5743679c2b701ca11977f6ca2f64

View on Chainz ↗

Height

#243,509

Difficulty

9.961569

Transactions

Size

229 B

Version

Bits

09f62961

Nonce

150

Timestamp

11/4/2013, 8:21:47 AM

Confirmations

6,599,329

Merkle Root

71f690acd2b8e7ab76a87e5c0b0afd9228b056d310abc172f4f6c78961f3b583

Transactions (1)

Coinbase71f690acd2b8e7…f6c78961f3b583

1 in → 2 out10.0600 XPM137 B

AZDUEbdS…RYKMRZET ALfEGCwh…VawujfMm

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.

9.641 × 10⁹⁸(99-digit number)

96419218520209232459…16183581709439826560

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

9.641 × 10⁹⁸(99-digit number)

96419218520209232459…16183581709439826559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.641 × 10⁹⁸(99-digit number)

96419218520209232459…16183581709439826561

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

1.928 × 10⁹⁹(100-digit number)

19283843704041846491…32367163418879653119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.928 × 10⁹⁹(100-digit number)

19283843704041846491…32367163418879653121

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

3.856 × 10⁹⁹(100-digit number)

38567687408083692983…64734326837759306239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.856 × 10⁹⁹(100-digit number)

38567687408083692983…64734326837759306241

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

7.713 × 10⁹⁹(100-digit number)

77135374816167385967…29468653675518612479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.713 × 10⁹⁹(100-digit number)

77135374816167385967…29468653675518612481

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

1.542 × 10¹⁰⁰(101-digit number)

15427074963233477193…58937307351037224959

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 243509

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 2e8b371cf827bbbbdefd0466c5b4c051324f5743679c2b701ca11977f6ca2f64

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 #243,509 on Chainz ↗

Block #243,509

Cookie Preferences