Home/Chain Registry/Block #199,843

Block #199,843

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/8/2013, 3:29:30 PM · Difficulty 9.8882 · 6,591,216 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43a827add1c2f089f35d4296f4725d7b3b394843ea8e113531e5b05b11e12990

View on Chainz ↗

Height

#199,843

Difficulty

9.888210

Transactions

Size

199 B

Version

Bits

09e361c2

Nonce

17,006

Timestamp

10/8/2013, 3:29:30 PM

Confirmations

6,591,216

Merkle Root

269faf9b478c2c186515658ad7a30e0be4a635ec267bddc0e69a32bd3f800a4d

Transactions (1)

Coinbase269faf9b478c2c…9a32bd3f800a4d

1 in → 1 out10.2100 XPM109 B

Ad4r8ZFu…p3oa5EDi

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.

3.776 × 10⁹⁵(96-digit number)

37762884422734878459…81364970186040823480

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

3.776 × 10⁹⁵(96-digit number)

37762884422734878459…81364970186040823479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.776 × 10⁹⁵(96-digit number)

37762884422734878459…81364970186040823481

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

7.552 × 10⁹⁵(96-digit number)

75525768845469756918…62729940372081646959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.552 × 10⁹⁵(96-digit number)

75525768845469756918…62729940372081646961

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

1.510 × 10⁹⁶(97-digit number)

15105153769093951383…25459880744163293919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.510 × 10⁹⁶(97-digit number)

15105153769093951383…25459880744163293921

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

3.021 × 10⁹⁶(97-digit number)

30210307538187902767…50919761488326587839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.021 × 10⁹⁶(97-digit number)

30210307538187902767…50919761488326587841

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

6.042 × 10⁹⁶(97-digit number)

60420615076375805534…01839522976653175679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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 199843

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 43a827add1c2f089f35d4296f4725d7b3b394843ea8e113531e5b05b11e12990

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 #199,843 on Chainz ↗