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Block #286,693

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 12:04:12 AM · Difficulty 9.9859 · 6,504,412 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

18265e64fc5ec4ced340df05b0c055ec54b107888fe15023bb3df2da3adfd849

View on Chainz ↗

Height

#286,693

Difficulty

9.985904

Transactions

Size

879 B

Version

Bits

09fc643b

Nonce

76,554

Timestamp

12/1/2013, 12:04:12 AM

Confirmations

6,504,412

Merkle Root

993fa0cfcac9dfe5e500b0c5e53d704d9804a4669301fe420f33b776fe7ddd47

Transactions (3)

Coinbase0cd720a1b6c341…38d0e0ce235b7c

1 in → 1 out10.0300 XPM110 B

AeKNrjNj…1NEq95Ta

0a446793f237cd…85cb2c8e33a39f

1 in → 1 out199.9900 XPM192 B

AH2frKqv…vGndmru6

a7ab3dbcebfc8e…a5d383f744c911

3 in → 1 out31.9900 XPM486 B

AVaYxnq9…6pQcS3fG

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.

4.246 × 10⁹⁷(98-digit number)

42469297221923413740…45509195211782410240

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

4.246 × 10⁹⁷(98-digit number)

42469297221923413740…45509195211782410239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.246 × 10⁹⁷(98-digit number)

42469297221923413740…45509195211782410241

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

8.493 × 10⁹⁷(98-digit number)

84938594443846827480…91018390423564820479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.493 × 10⁹⁷(98-digit number)

84938594443846827480…91018390423564820481

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

1.698 × 10⁹⁸(99-digit number)

16987718888769365496…82036780847129640959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.698 × 10⁹⁸(99-digit number)

16987718888769365496…82036780847129640961

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

3.397 × 10⁹⁸(99-digit number)

33975437777538730992…64073561694259281919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.397 × 10⁹⁸(99-digit number)

33975437777538730992…64073561694259281921

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

6.795 × 10⁹⁸(99-digit number)

67950875555077461984…28147123388518563839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.795 × 10⁹⁸(99-digit number)

67950875555077461984…28147123388518563841

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 286693

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 18265e64fc5ec4ced340df05b0c055ec54b107888fe15023bb3df2da3adfd849

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 #286,693 on Chainz ↗