Home/Chain Registry/Block #502,422

Block #502,422

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/20/2014, 10:08:39 AM · Difficulty 10.8071 · 6,323,752 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6fb5d1f5880aaa65067be4d69a5d06b414a5d3f45497c12933ca135136b10e23

View on Chainz ↗

Height

#502,422

Difficulty

10.807100

Transactions

Size

207 B

Version

Bits

0ace9e13

Nonce

472,333,249

Timestamp

4/20/2014, 10:08:39 AM

Confirmations

6,323,752

Merkle Root

35677e0ad6c002fcaecc809d09d1c209bd6962bdc3910268ac9d789fb5934e71

Transactions (1)

Coinbase35677e0ad6c002…9d789fb5934e71

1 in → 1 out8.5500 XPM116 B

AbwWkWZt…kawDhufa

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.

1.572 × 10⁹⁸(99-digit number)

15722445980425958870…41768117926411159040

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

1.572 × 10⁹⁸(99-digit number)

15722445980425958870…41768117926411159039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.572 × 10⁹⁸(99-digit number)

15722445980425958870…41768117926411159041

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

3.144 × 10⁹⁸(99-digit number)

31444891960851917741…83536235852822318079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.144 × 10⁹⁸(99-digit number)

31444891960851917741…83536235852822318081

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

6.288 × 10⁹⁸(99-digit number)

62889783921703835482…67072471705644636159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.288 × 10⁹⁸(99-digit number)

62889783921703835482…67072471705644636161

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

1.257 × 10⁹⁹(100-digit number)

12577956784340767096…34144943411289272319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.257 × 10⁹⁹(100-digit number)

12577956784340767096…34144943411289272321

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

2.515 × 10⁹⁹(100-digit number)

25155913568681534193…68289886822578544639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.515 × 10⁹⁹(100-digit number)

25155913568681534193…68289886822578544641

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 502422

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 6fb5d1f5880aaa65067be4d69a5d06b414a5d3f45497c12933ca135136b10e23

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 #502,422 on Chainz ↗

Block #502,422

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