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Block #509,622

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/25/2014, 4:30:08 AM · Difficulty 10.8202 · 6,317,150 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

490029ca8aba544fa117c3b1e8de32d4635c469baf4617bfa5436eabddb4c945

View on Chainz ↗

Height

#509,622

Difficulty

10.820232

Transactions

Size

428 B

Version

Bits

0ad1fab8

Nonce

194,578,947

Timestamp

4/25/2014, 4:30:08 AM

Confirmations

6,317,150

Merkle Root

a69487898e787839b416132e4c908fb98946c6a4fd0c6234ee861800bffd3b7c

Transactions (2)

Coinbasedea41baf624692…16e09fb449561a

1 in → 1 out8.5400 XPM110 B

APAhEFVd…iM24JQLp

e9fe4648b9febe…aab812ae8bbfd7

1 in → 2 out3935.4371 XPM226 B

AbZymyRQ…YZm38rjw APkJVRx9…qLCcNZnt

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.

4.520 × 10⁹⁹(100-digit number)

45209438041795951452…30260809652425963520

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

4.520 × 10⁹⁹(100-digit number)

45209438041795951452…30260809652425963519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.520 × 10⁹⁹(100-digit number)

45209438041795951452…30260809652425963521

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

9.041 × 10⁹⁹(100-digit number)

90418876083591902905…60521619304851927039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.041 × 10⁹⁹(100-digit number)

90418876083591902905…60521619304851927041

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

1.808 × 10¹⁰⁰(101-digit number)

18083775216718380581…21043238609703854079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.808 × 10¹⁰⁰(101-digit number)

18083775216718380581…21043238609703854081

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

3.616 × 10¹⁰⁰(101-digit number)

36167550433436761162…42086477219407708159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.616 × 10¹⁰⁰(101-digit number)

36167550433436761162…42086477219407708161

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

7.233 × 10¹⁰⁰(101-digit number)

72335100866873522324…84172954438815416319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.233 × 10¹⁰⁰(101-digit number)

72335100866873522324…84172954438815416321

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 509622

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 490029ca8aba544fa117c3b1e8de32d4635c469baf4617bfa5436eabddb4c945

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 #509,622 on Chainz ↗

Block #509,622

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