Home/Chain Registry/Block #199,574

Block #199,574

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/8/2013, 11:21:46 AM · Difficulty 9.8878 · 6,612,575 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

75c39b1ea6958858e65bcfefa2df31089a89b3bd89cb066d888925f8629deb0f

View on Chainz ↗

Height

#199,574

Difficulty

9.887752

Transactions

Size

3.34 KB

Version

Bits

09e343ba

Nonce

1,165,043,285

Timestamp

10/8/2013, 11:21:46 AM

Confirmations

6,612,575

Merkle Root

11d0306c158a42f6cc8ea43f4c87e77a51528466769f61acebb079df75a6f0ae

Transactions (1)

Coinbase11d0306c158a42…b079df75a6f0ae

1 in → 96 out10.1700 XPM3.25 KB

AQWqri7X…mhX7yWLi AR7hUyNW…iuooRCti AQeTwBRF…bqV1qrYX ANBtDhv7…saWQoBRP ATeGzPEb…fEYhKxfs

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.

1.525 × 10⁹⁷(98-digit number)

15257169303024505918…92615023365829626880

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

1.525 × 10⁹⁷(98-digit number)

15257169303024505918…92615023365829626879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.525 × 10⁹⁷(98-digit number)

15257169303024505918…92615023365829626881

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

3.051 × 10⁹⁷(98-digit number)

30514338606049011836…85230046731659253759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.051 × 10⁹⁷(98-digit number)

30514338606049011836…85230046731659253761

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

6.102 × 10⁹⁷(98-digit number)

61028677212098023672…70460093463318507519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.102 × 10⁹⁷(98-digit number)

61028677212098023672…70460093463318507521

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

1.220 × 10⁹⁸(99-digit number)

12205735442419604734…40920186926637015039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.220 × 10⁹⁸(99-digit number)

12205735442419604734…40920186926637015041

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

2.441 × 10⁹⁸(99-digit number)

24411470884839209468…81840373853274030079

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 199574

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 75c39b1ea6958858e65bcfefa2df31089a89b3bd89cb066d888925f8629deb0f

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 #199,574 on Chainz ↗

Block #199,574

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