Home/Chain Registry/Block #318,223

Block #318,223

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/18/2013, 5:24:23 AM · Difficulty 10.1590 · 6,474,546 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f47ee927b3a309e8cf60f515d2aa253d0c830546507ebd8733a62ceee1569116

View on Chainz ↗

Height

#318,223

Difficulty

10.158958

Transactions

Size

205 B

Version

Bits

0a28b180

Nonce

44,360

Timestamp

12/18/2013, 5:24:23 AM

Confirmations

6,474,546

Merkle Root

d9090cfd5e8af92dd4df516440fd693f99ed66e701a3af2f1dc31cbdbc4eed64

Transactions (1)

Coinbased9090cfd5e8af9…c31cbdbc4eed64

1 in → 1 out9.6700 XPM116 B

AbwWkWZt…kawDhufa

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.

1.036 × 10⁹³(94-digit number)

10367902943779922683…93430322028692602040

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

1.036 × 10⁹³(94-digit number)

10367902943779922683…93430322028692602039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.036 × 10⁹³(94-digit number)

10367902943779922683…93430322028692602041

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

2.073 × 10⁹³(94-digit number)

20735805887559845367…86860644057385204079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.073 × 10⁹³(94-digit number)

20735805887559845367…86860644057385204081

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

4.147 × 10⁹³(94-digit number)

41471611775119690734…73721288114770408159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.147 × 10⁹³(94-digit number)

41471611775119690734…73721288114770408161

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

8.294 × 10⁹³(94-digit number)

82943223550239381469…47442576229540816319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.294 × 10⁹³(94-digit number)

82943223550239381469…47442576229540816321

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

1.658 × 10⁹⁴(95-digit number)

16588644710047876293…94885152459081632639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.658 × 10⁹⁴(95-digit number)

16588644710047876293…94885152459081632641

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 318223

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 f47ee927b3a309e8cf60f515d2aa253d0c830546507ebd8733a62ceee1569116

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 #318,223 on Chainz ↗