Home/Chain Registry/Block #43,202

Block #43,202

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 8:24:33 PM · Difficulty 8.6497 · 6,746,717 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f1cb3af56aec8c641c6545faa35cffd1522edaee8217c2e7be1a6f757971e022

View on Chainz ↗

Height

#43,202

Difficulty

8.649690

Transactions

Size

364 B

Version

Bits

08a65215

Nonce

273

Timestamp

7/14/2013, 8:24:33 PM

Confirmations

6,746,717

Merkle Root

031decd4968693028adaef84bd4bb563daffde2eea1adade15697d83143ef752

Transactions (2)

Coinbasefc3fd371957a19…5927b0ff4ddb24

1 in → 1 out13.3600 XPM109 B

ASUvBvCm…YXYrMmir

d2b0ec0fb9835a…c1dd8b8d41ebae

1 in → 1 out15.6700 XPM159 B

AT75Y59F…25dGF43a

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.

4.656 × 10¹⁰⁸(109-digit number)

46569465826926776580…56955701607133635000

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

4.656 × 10¹⁰⁸(109-digit number)

46569465826926776580…56955701607133634999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.656 × 10¹⁰⁸(109-digit number)

46569465826926776580…56955701607133635001

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

9.313 × 10¹⁰⁸(109-digit number)

93138931653853553160…13911403214267269999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.313 × 10¹⁰⁸(109-digit number)

93138931653853553160…13911403214267270001

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

1.862 × 10¹⁰⁹(110-digit number)

18627786330770710632…27822806428534539999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.862 × 10¹⁰⁹(110-digit number)

18627786330770710632…27822806428534540001

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

3.725 × 10¹⁰⁹(110-digit number)

37255572661541421264…55645612857069079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.725 × 10¹⁰⁹(110-digit number)

37255572661541421264…55645612857069080001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

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 43202

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 f1cb3af56aec8c641c6545faa35cffd1522edaee8217c2e7be1a6f757971e022

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 #43,202 on Chainz ↗