Home/Chain Registry/Block #355,023

Block #355,023

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/11/2014, 9:30:28 PM · Difficulty 10.3552 · 6,471,287 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1fe660c325e48de95796bac85220a2da715bc3b441cf400d259b63e93abc0a42

View on Chainz ↗

Height

#355,023

Difficulty

10.355165

Transactions

Size

209 B

Version

Bits

0a5aec19

Nonce

1,980

Timestamp

1/11/2014, 9:30:28 PM

Confirmations

6,471,287

Merkle Root

79a8e1b1c532c67b0a97de0742378e89fd19c9d85878377efccb3856e34a25d9

Transactions (1)

Coinbase79a8e1b1c532c6…cb3856e34a25d9

1 in → 1 out9.3100 XPM116 B

AbwWkWZt…kawDhufa

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.

6.121 × 10¹⁰⁰(101-digit number)

61212677605148369134…63722794230091284480

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

6.121 × 10¹⁰⁰(101-digit number)

61212677605148369134…63722794230091284479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.121 × 10¹⁰⁰(101-digit number)

61212677605148369134…63722794230091284481

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

1.224 × 10¹⁰¹(102-digit number)

12242535521029673826…27445588460182568959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.224 × 10¹⁰¹(102-digit number)

12242535521029673826…27445588460182568961

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

2.448 × 10¹⁰¹(102-digit number)

24485071042059347653…54891176920365137919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.448 × 10¹⁰¹(102-digit number)

24485071042059347653…54891176920365137921

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

4.897 × 10¹⁰¹(102-digit number)

48970142084118695307…09782353840730275839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.897 × 10¹⁰¹(102-digit number)

48970142084118695307…09782353840730275841

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

9.794 × 10¹⁰¹(102-digit number)

97940284168237390614…19564707681460551679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.794 × 10¹⁰¹(102-digit number)

97940284168237390614…19564707681460551681

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 355023

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 1fe660c325e48de95796bac85220a2da715bc3b441cf400d259b63e93abc0a42

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 #355,023 on Chainz ↗

Block #355,023

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