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Block #414,532

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/22/2014, 2:07:49 AM · Difficulty 10.4022 · 6,397,533 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e13990242548fbf3da514d2a115ea5316ec774c799eff8f1465310fc3aad57f4

View on Chainz ↗

Height

#414,532

Difficulty

10.402176

Transactions

Size

1.90 KB

Version

Bits

0a66f500

Nonce

320,889

Timestamp

2/22/2014, 2:07:49 AM

Confirmations

6,397,533

Merkle Root

3063d5af45b17b004b98b3f34cfbe5ace0e7c72a2cd46085e3c5d58e9b085637

Transactions (3)

Coinbase9bade67ca6374d…ceb918d552f49b

1 in → 1 out9.2600 XPM110 B

AeKNrjNj…1NEq95Ta

7bfddbde2e309c…301d9fdbd4c513

9 in → 9 out28.2356 XPM1.51 KB

AdB9yYJ5…odZ1GvMr AZdEFDaP…C5X9uRee AJ2a8S3W…tqXNT8d1 ANQKf2g4…29NaVj23 AZ3PWPr3…T7o8gD2E

7bda32dd7340c4…27819eb7f008eb

1 in → 1 out3.0200 XPM193 B

AdVQpbsD…qCfipjk4

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.

1.296 × 10¹⁰¹(102-digit number)

12960226588191874643…32602846040997358400

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

1.296 × 10¹⁰¹(102-digit number)

12960226588191874643…32602846040997358399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.296 × 10¹⁰¹(102-digit number)

12960226588191874643…32602846040997358401

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

2.592 × 10¹⁰¹(102-digit number)

25920453176383749286…65205692081994716799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.592 × 10¹⁰¹(102-digit number)

25920453176383749286…65205692081994716801

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

5.184 × 10¹⁰¹(102-digit number)

51840906352767498573…30411384163989433599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.184 × 10¹⁰¹(102-digit number)

51840906352767498573…30411384163989433601

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

1.036 × 10¹⁰²(103-digit number)

10368181270553499714…60822768327978867199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.036 × 10¹⁰²(103-digit number)

10368181270553499714…60822768327978867201

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

2.073 × 10¹⁰²(103-digit number)

20736362541106999429…21645536655957734399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.073 × 10¹⁰²(103-digit number)

20736362541106999429…21645536655957734401

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 414532

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 e13990242548fbf3da514d2a115ea5316ec774c799eff8f1465310fc3aad57f4

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 #414,532 on Chainz ↗

Block #414,532

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