Home/Chain Registry/Block #278,262

Block #278,262

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 10:04:41 PM · Difficulty 9.9685 · 6,515,236 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

31ea8b0d36e34fc9de56b84070f236b754bebbb1770e22ae445030cd47aab24e

View on Chainz ↗

Height

#278,262

Difficulty

9.968474

Transactions

Size

207 B

Version

Bits

09f7edeb

Nonce

103,500

Timestamp

11/27/2013, 10:04:41 PM

Confirmations

6,515,236

Merkle Root

3aa42ba78773b87bb432bd501dcf44059ab93d836d6201bc3059e6c7040e8080

Transactions (1)

Coinbase3aa42ba78773b8…59e6c7040e8080

1 in → 1 out10.0500 XPM116 B

AcLBm5Z9…S683d7c3

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.

1.925 × 10⁹⁶(97-digit number)

19255535475337552704…09776587064898260480

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

1.925 × 10⁹⁶(97-digit number)

19255535475337552704…09776587064898260479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.925 × 10⁹⁶(97-digit number)

19255535475337552704…09776587064898260481

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

3.851 × 10⁹⁶(97-digit number)

38511070950675105409…19553174129796520959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.851 × 10⁹⁶(97-digit number)

38511070950675105409…19553174129796520961

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

7.702 × 10⁹⁶(97-digit number)

77022141901350210818…39106348259593041919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.702 × 10⁹⁶(97-digit number)

77022141901350210818…39106348259593041921

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

1.540 × 10⁹⁷(98-digit number)

15404428380270042163…78212696519186083839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.540 × 10⁹⁷(98-digit number)

15404428380270042163…78212696519186083841

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

3.080 × 10⁹⁷(98-digit number)

30808856760540084327…56425393038372167679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.080 × 10⁹⁷(98-digit number)

30808856760540084327…56425393038372167681

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 278262

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 31ea8b0d36e34fc9de56b84070f236b754bebbb1770e22ae445030cd47aab24e

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 #278,262 on Chainz ↗