Home/Chain Registry/Block #209,342

Block #209,342

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/14/2013, 12:56:23 PM · Difficulty 9.9092 · 6,591,689 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0f385eb28de8af98c044785d7c04558a8df1d3b11d1500e0307419ecbf048fcb

View on Chainz ↗

Height

#209,342

Difficulty

9.909163

Transactions

Size

583 B

Version

Bits

09e8bee9

Nonce

15,032

Timestamp

10/14/2013, 12:56:23 PM

Confirmations

6,591,689

Merkle Root

406cf28d4ab92096f506ecb6e433b63a8e25f91104a67dbb1f53cd892db494d1

Transactions (3)

Coinbased60a1e3467abc0…faf1ebe4b54e37

1 in → 1 out10.1900 XPM109 B

ANDqQMEx…AAmWQbv8

8d027752621194…2b4e7b255e8972

1 in → 2 out10.1900 XPM191 B

AaMRUFMG…S11BNFrC APm164Mu…KuPrCC6c

225422dc186df3…87dc557f14c38c

1 in → 1 out5.0900 XPM192 B

AeguK5Ai…CLUqoF9q

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.

1.478 × 10⁹⁶(97-digit number)

14788183746672612184…90708563548352838080

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

1.478 × 10⁹⁶(97-digit number)

14788183746672612184…90708563548352838079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.478 × 10⁹⁶(97-digit number)

14788183746672612184…90708563548352838081

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

2.957 × 10⁹⁶(97-digit number)

29576367493345224368…81417127096705676159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.957 × 10⁹⁶(97-digit number)

29576367493345224368…81417127096705676161

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

5.915 × 10⁹⁶(97-digit number)

59152734986690448737…62834254193411352319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.915 × 10⁹⁶(97-digit number)

59152734986690448737…62834254193411352321

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

1.183 × 10⁹⁷(98-digit number)

11830546997338089747…25668508386822704639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.183 × 10⁹⁷(98-digit number)

11830546997338089747…25668508386822704641

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

2.366 × 10⁹⁷(98-digit number)

23661093994676179494…51337016773645409279

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 209342

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 0f385eb28de8af98c044785d7c04558a8df1d3b11d1500e0307419ecbf048fcb

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 #209,342 on Chainz ↗