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Block #422,403

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 4:58:25 PM · Difficulty 10.3794 · 6,404,881 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d052f099f378823468f0f4aad2f1e219522f986b4b22bfde3cc8c677e502d93

View on Chainz ↗

Height

#422,403

Difficulty

10.379351

Transactions

Size

972 B

Version

Bits

0a611d23

Nonce

7,652

Timestamp

2/27/2014, 4:58:25 PM

Confirmations

6,404,881

Merkle Root

448c8104473f1a51610dff6355c073698a01aaa445e0a10330e806421bededd2

Transactions (1)

Coinbase448c8104473f1a…e806421bededd2

1 in → 24 out9.2700 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AKV2FjBH…nZo6NrFp AGKhfQo2…h7fBXLX6 AbCoYyit…3RWVcAeS

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.

1.517 × 10¹⁰¹(102-digit number)

15178872401308387716…45464566886080463040

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

1.517 × 10¹⁰¹(102-digit number)

15178872401308387716…45464566886080463039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.517 × 10¹⁰¹(102-digit number)

15178872401308387716…45464566886080463041

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

3.035 × 10¹⁰¹(102-digit number)

30357744802616775432…90929133772160926079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.035 × 10¹⁰¹(102-digit number)

30357744802616775432…90929133772160926081

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

6.071 × 10¹⁰¹(102-digit number)

60715489605233550864…81858267544321852159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.071 × 10¹⁰¹(102-digit number)

60715489605233550864…81858267544321852161

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

1.214 × 10¹⁰²(103-digit number)

12143097921046710172…63716535088643704319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.214 × 10¹⁰²(103-digit number)

12143097921046710172…63716535088643704321

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

2.428 × 10¹⁰²(103-digit number)

24286195842093420345…27433070177287408639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.428 × 10¹⁰²(103-digit number)

24286195842093420345…27433070177287408641

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 422403

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 2d052f099f378823468f0f4aad2f1e219522f986b4b22bfde3cc8c677e502d93

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 #422,403 on Chainz ↗

Block #422,403

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