Home/Chain Registry/Block #483,315

Block #483,315

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/9/2014, 11:45:52 PM · Difficulty 10.5611 · 6,317,379 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

19aeb0d4741ba1fba3d5369cf76dc8cf5f2bca74a99f2809281f01f7701dfa51

View on Chainz ↗

Height

#483,315

Difficulty

10.561087

Transactions

Size

652 B

Version

Bits

0a8fa361

Nonce

171,696

Timestamp

4/9/2014, 11:45:52 PM

Confirmations

6,317,379

Merkle Root

4e373dda71b1d8cf4a76524ec927b83e7fd05889260ee5009df35c14f5e4df1c

Transactions (3)

Coinbasea3bb70a9e4fed7…329c005b0d70c0

1 in → 1 out8.9700 XPM109 B

AeKNrjNj…1NEq95Ta

0422e7db731ebf…66bbbb2593de75

1 in → 2 out9.0200 XPM225 B

AaaNr3Rc…r4yNDU6C AKxsEUtx…B9Mfu8PP

04ca0e947fa596…46b0db0d68c6d6

1 in → 2 out8.5084 XPM225 B

AV5worwK…euUejyW9 AMU8nEj9…Eo32pqxr

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.

1.964 × 10¹⁰¹(102-digit number)

19641985078725222514…90444113755815443520

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

1.964 × 10¹⁰¹(102-digit number)

19641985078725222514…90444113755815443519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.964 × 10¹⁰¹(102-digit number)

19641985078725222514…90444113755815443521

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

3.928 × 10¹⁰¹(102-digit number)

39283970157450445028…80888227511630887039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.928 × 10¹⁰¹(102-digit number)

39283970157450445028…80888227511630887041

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

7.856 × 10¹⁰¹(102-digit number)

78567940314900890057…61776455023261774079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.856 × 10¹⁰¹(102-digit number)

78567940314900890057…61776455023261774081

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

1.571 × 10¹⁰²(103-digit number)

15713588062980178011…23552910046523548159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.571 × 10¹⁰²(103-digit number)

15713588062980178011…23552910046523548161

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

3.142 × 10¹⁰²(103-digit number)

31427176125960356023…47105820093047096319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.142 × 10¹⁰²(103-digit number)

31427176125960356023…47105820093047096321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

6.285 × 10¹⁰²(103-digit number)

62854352251920712046…94211640186094192639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 483315

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 19aeb0d4741ba1fba3d5369cf76dc8cf5f2bca74a99f2809281f01f7701dfa51

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 #483,315 on Chainz ↗