Home/Chain Registry/Block #198,215

Block #198,215

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/7/2013, 2:59:55 PM · Difficulty 9.8846 · 6,593,621 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1799b4ec3b994e1f33b831b1e5d94a0c0ad07e090a702116138e3d9987ce4176

View on Chainz ↗

Height

#198,215

Difficulty

9.884584

Transactions

Size

199 B

Version

Bits

09e27420

Nonce

11,475

Timestamp

10/7/2013, 2:59:55 PM

Confirmations

6,593,621

Merkle Root

19f75007b3129c579b30d1e1e4ab653a0a943d889503b717d6f6be99bfe7b9ce

Transactions (1)

Coinbase19f75007b3129c…f6be99bfe7b9ce

1 in → 1 out10.2200 XPM109 B

AY44Ahff…sBrkUN8J

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.

7.841 × 10⁹³(94-digit number)

78419451467225029752…54074104124611547400

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

7.841 × 10⁹³(94-digit number)

78419451467225029752…54074104124611547399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.841 × 10⁹³(94-digit number)

78419451467225029752…54074104124611547401

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

1.568 × 10⁹⁴(95-digit number)

15683890293445005950…08148208249223094799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.568 × 10⁹⁴(95-digit number)

15683890293445005950…08148208249223094801

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

3.136 × 10⁹⁴(95-digit number)

31367780586890011900…16296416498446189599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.136 × 10⁹⁴(95-digit number)

31367780586890011900…16296416498446189601

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

6.273 × 10⁹⁴(95-digit number)

62735561173780023801…32592832996892379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.273 × 10⁹⁴(95-digit number)

62735561173780023801…32592832996892379201

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

1.254 × 10⁹⁵(96-digit number)

12547112234756004760…65185665993784758399

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 198215

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 1799b4ec3b994e1f33b831b1e5d94a0c0ad07e090a702116138e3d9987ce4176

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 #198,215 on Chainz ↗