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Block #320,203

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/19/2013, 12:22:28 PM · Difficulty 10.1795 · 6,480,768 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d92d047cd07082ca9ac5c6c6a03e28129a341424bf2a102343ef7e70130d14cf

View on Chainz ↗

Height

#320,203

Difficulty

10.179455

Transactions

Size

1.72 KB

Version

Bits

0a2df0c5

Nonce

67,428

Timestamp

12/19/2013, 12:22:28 PM

Confirmations

6,480,768

Merkle Root

fc7b81530cef8dfa2a74443797ea85f126eb5cda1c7901235b9fab519a110537

Transactions (4)

Coinbase44d04e9ec8862b…3dae392b03cd77

1 in → 1 out9.6700 XPM109 B

AJgAb7rz…PxxnjM15

3350d6c02b3308…d3f4a5fa6e8049

3 in → 2 out6.3761 XPM523 B

AdMCgUoY…ArDPJ6iU Aej6WjTC…EupgQanK

43712b2101cade…e910450795addb

1 in → 2 out1.5075 XPM226 B

AWUK71Ex…YfskuY2j AMisE9oH…ejCxi6Xe

3aba26fcf24bd4…59ff559c515956

5 in → 2 out2.0111 XPM814 B

AYyPgD7h…DKx6JrPs AcaTXqYM…fy1NEvve

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.

1.031 × 10⁹⁹(100-digit number)

10318879478733096715…08019580799871195220

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

1.031 × 10⁹⁹(100-digit number)

10318879478733096715…08019580799871195219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.031 × 10⁹⁹(100-digit number)

10318879478733096715…08019580799871195221

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

2.063 × 10⁹⁹(100-digit number)

20637758957466193430…16039161599742390439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.063 × 10⁹⁹(100-digit number)

20637758957466193430…16039161599742390441

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

4.127 × 10⁹⁹(100-digit number)

41275517914932386860…32078323199484780879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.127 × 10⁹⁹(100-digit number)

41275517914932386860…32078323199484780881

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

8.255 × 10⁹⁹(100-digit number)

82551035829864773721…64156646398969561759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.255 × 10⁹⁹(100-digit number)

82551035829864773721…64156646398969561761

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

1.651 × 10¹⁰⁰(101-digit number)

16510207165972954744…28313292797939123519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.651 × 10¹⁰⁰(101-digit number)

16510207165972954744…28313292797939123521

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 320203

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 d92d047cd07082ca9ac5c6c6a03e28129a341424bf2a102343ef7e70130d14cf

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 #320,203 on Chainz ↗