Home/Chain Registry/Block #143,023

Block #143,023

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/31/2013, 8:59:24 AM · Difficulty 9.8373 · 6,646,892 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ac8ff406c60fde36524e1fccfdd8f99579ef919470a62593707a607a5a3b3d05

View on Chainz ↗

Height

#143,023

Difficulty

9.837335

Transactions

Size

206 B

Version

Bits

09d65b99

Nonce

245

Timestamp

8/31/2013, 8:59:24 AM

Confirmations

6,646,892

Merkle Root

8dac101023941865fa01cf673fe5bfed6fce95883068352bd07d7284e922c016

Transactions (1)

Coinbase8dac1010239418…7d7284e922c016

1 in → 1 out10.3200 XPM110 B

AGfzg5J3…atiLkF4X

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.

1.481 × 10¹⁰⁹(110-digit number)

14814560971876748471…39523803550524695130

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

1.481 × 10¹⁰⁹(110-digit number)

14814560971876748471…39523803550524695129

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.481 × 10¹⁰⁹(110-digit number)

14814560971876748471…39523803550524695131

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

2.962 × 10¹⁰⁹(110-digit number)

29629121943753496942…79047607101049390259

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.962 × 10¹⁰⁹(110-digit number)

29629121943753496942…79047607101049390261

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

5.925 × 10¹⁰⁹(110-digit number)

59258243887506993884…58095214202098780519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.925 × 10¹⁰⁹(110-digit number)

59258243887506993884…58095214202098780521

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

1.185 × 10¹¹⁰(111-digit number)

11851648777501398776…16190428404197561039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.185 × 10¹¹⁰(111-digit number)

11851648777501398776…16190428404197561041

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

2.370 × 10¹¹⁰(111-digit number)

23703297555002797553…32380856808395122079

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 143023

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 ac8ff406c60fde36524e1fccfdd8f99579ef919470a62593707a607a5a3b3d05

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 #143,023 on Chainz ↗