Home/Chain Registry/Block #203,257

Block #203,257

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/10/2013, 5:54:32 PM · Difficulty 9.8968 · 6,586,815 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07acaf6c0f6d81eb4cc076f469f494599167cd524da7ae03802e33e4cede9e18

View on Chainz ↗

Height

#203,257

Difficulty

9.896833

Transactions

Size

201 B

Version

Bits

09e596d4

Nonce

1,179

Timestamp

10/10/2013, 5:54:32 PM

Confirmations

6,586,815

Merkle Root

e460dad85ade5e9c34407e65eea09e578216df403eec472a0902b5eac1d769b6

Transactions (1)

Coinbasee460dad85ade5e…02b5eac1d769b6

1 in → 1 out10.1900 XPM109 B

ASUFTk3k…6G1byU7n

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.

7.189 × 10⁹⁸(99-digit number)

71899887268660746519…25116623264869121920

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

7.189 × 10⁹⁸(99-digit number)

71899887268660746519…25116623264869121919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.189 × 10⁹⁸(99-digit number)

71899887268660746519…25116623264869121921

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

1.437 × 10⁹⁹(100-digit number)

14379977453732149303…50233246529738243839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.437 × 10⁹⁹(100-digit number)

14379977453732149303…50233246529738243841

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

2.875 × 10⁹⁹(100-digit number)

28759954907464298607…00466493059476487679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.875 × 10⁹⁹(100-digit number)

28759954907464298607…00466493059476487681

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

5.751 × 10⁹⁹(100-digit number)

57519909814928597215…00932986118952975359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.751 × 10⁹⁹(100-digit number)

57519909814928597215…00932986118952975361

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

1.150 × 10¹⁰⁰(101-digit number)

11503981962985719443…01865972237905950719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.150 × 10¹⁰⁰(101-digit number)

11503981962985719443…01865972237905950721

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 203257

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 07acaf6c0f6d81eb4cc076f469f494599167cd524da7ae03802e33e4cede9e18

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 #203,257 on Chainz ↗