Home/Chain Registry/Block #198,464

Block #198,464

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/7/2013, 6:16:33 PM · Difficulty 9.8859 · 6,593,950 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

701a2111b33d3cd9afcafbf85eb3bc1e32d36aed19c3add6d1302277218c44bc

View on Chainz ↗

Height

#198,464

Difficulty

9.885933

Transactions

Size

206 B

Version

Bits

09e2cc84

Nonce

602

Timestamp

10/7/2013, 6:16:33 PM

Confirmations

6,593,950

Merkle Root

3188cefdec027172d4dc8697e1febade4a97f8796a4c8f8b3fa33fb84ef788a0

Transactions (1)

Coinbase3188cefdec0271…a33fb84ef788a0

1 in → 1 out10.2200 XPM116 B

AcLBm5Z9…S683d7c3

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.

3.212 × 10⁹⁴(95-digit number)

32123771621409658430…31236408255418507520

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

3.212 × 10⁹⁴(95-digit number)

32123771621409658430…31236408255418507519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.212 × 10⁹⁴(95-digit number)

32123771621409658430…31236408255418507521

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

6.424 × 10⁹⁴(95-digit number)

64247543242819316861…62472816510837015039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.424 × 10⁹⁴(95-digit number)

64247543242819316861…62472816510837015041

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

1.284 × 10⁹⁵(96-digit number)

12849508648563863372…24945633021674030079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.284 × 10⁹⁵(96-digit number)

12849508648563863372…24945633021674030081

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

2.569 × 10⁹⁵(96-digit number)

25699017297127726744…49891266043348060159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.569 × 10⁹⁵(96-digit number)

25699017297127726744…49891266043348060161

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

5.139 × 10⁹⁵(96-digit number)

51398034594255453488…99782532086696120319

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 198464

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 701a2111b33d3cd9afcafbf85eb3bc1e32d36aed19c3add6d1302277218c44bc

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 #198,464 on Chainz ↗