Home/Chain Registry/Block #237,268

Block #237,268

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 10:56:33 PM · Difficulty 9.9494 · 6,587,361 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1bfa3b76087004f6c705b59ad01a359e1ab00a6201dc05549648b9b912a4fc27

View on Chainz ↗

Height

#237,268

Difficulty

9.949415

Transactions

Size

1.84 KB

Version

Bits

09f30cd5

Nonce

193,395

Timestamp

10/31/2013, 10:56:33 PM

Confirmations

6,587,361

Merkle Root

50cc6f720018215f64f77a32182c9d57abe91ab315b63540c8755fe3e48371ce

Transactions (1)

Coinbase50cc6f72001821…755fe3e48371ce

1 in → 51 out10.0700 XPM1.75 KB

Ac5sZcdP…kzV4eckG ANWcCA1W…FYxSHbqJ ANuKx9Ke…wm7nrBRq AQtzUSwq…htAuF3yC ANUaggy4…MWdrertQ

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.

8.653 × 10⁸⁹(90-digit number)

86535126214512555992…47252764821602412140

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

8.653 × 10⁸⁹(90-digit number)

86535126214512555992…47252764821602412139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.653 × 10⁸⁹(90-digit number)

86535126214512555992…47252764821602412141

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

1.730 × 10⁹⁰(91-digit number)

17307025242902511198…94505529643204824279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.730 × 10⁹⁰(91-digit number)

17307025242902511198…94505529643204824281

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

3.461 × 10⁹⁰(91-digit number)

34614050485805022397…89011059286409648559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.461 × 10⁹⁰(91-digit number)

34614050485805022397…89011059286409648561

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

6.922 × 10⁹⁰(91-digit number)

69228100971610044794…78022118572819297119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.922 × 10⁹⁰(91-digit number)

69228100971610044794…78022118572819297121

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

1.384 × 10⁹¹(92-digit number)

13845620194322008958…56044237145638594239

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 237268

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 1bfa3b76087004f6c705b59ad01a359e1ab00a6201dc05549648b9b912a4fc27

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 #237,268 on Chainz ↗

Block #237,268

Cookie Preferences