Home/Chain Registry/Block #352,198

Block #352,198

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2014, 4:48:22 AM · Difficulty 10.3042 · 6,449,606 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f7671bc7c2ddf1d11020b601985c6142bd832340811216fa45f3caaa1ecae79f

View on Chainz ↗

Height

#352,198

Difficulty

10.304231

Transactions

Size

1.40 KB

Version

Bits

0a4de21d

Nonce

238,687

Timestamp

1/10/2014, 4:48:22 AM

Confirmations

6,449,606

Merkle Root

4f02d4e252937954a84e7eed703bb26bed1fc3bb25c1c9aff3ad6d27c2464262

Transactions (2)

Coinbase25a13e76fc95ee…252d9ddf38f4ef

1 in → 11 out9.4100 XPM437 B

AMQC4aya…c4ptxi3K AN9emqpK…WEnrfX7s AR13RD7s…sfkxQZ92 Acs9SHrk…QJSB8SFG AZqjMFvv…G8aw2zC8

c8778182801137…68c09bbdaf9d64

4 in → 13 out37.9400 XPM907 B

APtbY7Fb…dMzBxJaJ AZxi9Pfz…SKPY4V4N ASW9Q8Bj…iRBBHR2e ALTkzyX5…UeKoYPzu AazfaUAJ…WaQjuUwm

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.

1.164 × 10⁹⁵(96-digit number)

11648093406560603246…86832518397723756320

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

1.164 × 10⁹⁵(96-digit number)

11648093406560603246…86832518397723756319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.164 × 10⁹⁵(96-digit number)

11648093406560603246…86832518397723756321

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

2.329 × 10⁹⁵(96-digit number)

23296186813121206493…73665036795447512639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.329 × 10⁹⁵(96-digit number)

23296186813121206493…73665036795447512641

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

4.659 × 10⁹⁵(96-digit number)

46592373626242412986…47330073590895025279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.659 × 10⁹⁵(96-digit number)

46592373626242412986…47330073590895025281

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

9.318 × 10⁹⁵(96-digit number)

93184747252484825972…94660147181790050559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.318 × 10⁹⁵(96-digit number)

93184747252484825972…94660147181790050561

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

1.863 × 10⁹⁶(97-digit number)

18636949450496965194…89320294363580101119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.863 × 10⁹⁶(97-digit number)

18636949450496965194…89320294363580101121

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 352198

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 f7671bc7c2ddf1d11020b601985c6142bd832340811216fa45f3caaa1ecae79f

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 #352,198 on Chainz ↗