Home/Chain Registry/Block #262,832

Block #262,832

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/17/2013, 6:06:37 AM · Difficulty 9.9676 · 6,535,556 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

50361101b4b5690244c9399f9992108b575da8ca1016feb5052338ea9c9bb253

View on Chainz ↗

Height

#262,832

Difficulty

9.967600

Transactions

Size

1.81 KB

Version

Bits

09f7b49e

Nonce

284,534

Timestamp

11/17/2013, 6:06:37 AM

Confirmations

6,535,556

Merkle Root

3f721abfa590e85ea52d823154fb477c8682d454f6d19efd19fb23af76bd7806

Transactions (1)

Coinbase3f721abfa590e8…fb23af76bd7806

1 in → 50 out10.0300 XPM1.72 KB

Ae7UyoY4…DtgAv9cY AFqKfjez…qX9Ace3g AKXeSXzu…yeuNjvhB AQtzUSwq…htAuF3yC AN4KokSc…8oFYPA8o

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.

8.564 × 10⁹¹(92-digit number)

85649388997508699484…34959572745178333700

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

8.564 × 10⁹¹(92-digit number)

85649388997508699484…34959572745178333699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.564 × 10⁹¹(92-digit number)

85649388997508699484…34959572745178333701

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

1.712 × 10⁹²(93-digit number)

17129877799501739896…69919145490356667399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.712 × 10⁹²(93-digit number)

17129877799501739896…69919145490356667401

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

3.425 × 10⁹²(93-digit number)

34259755599003479793…39838290980713334799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.425 × 10⁹²(93-digit number)

34259755599003479793…39838290980713334801

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

6.851 × 10⁹²(93-digit number)

68519511198006959587…79676581961426669599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.851 × 10⁹²(93-digit number)

68519511198006959587…79676581961426669601

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

1.370 × 10⁹³(94-digit number)

13703902239601391917…59353163922853339199

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 262832

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 50361101b4b5690244c9399f9992108b575da8ca1016feb5052338ea9c9bb253

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 #262,832 on Chainz ↗