Home/Chain Registry/Block #143,019

Block #143,019

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/31/2013, 8:55:07 AM · Difficulty 9.8373 · 6,647,961 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1a719a2e1f263dc9778cd1a85b47607e0cdafbb379e67c45f70381389d42f945

View on Chainz ↗

Height

#143,019

Difficulty

9.837314

Transactions

Size

198 B

Version

Bits

09d65a2e

Nonce

23,368

Timestamp

8/31/2013, 8:55:07 AM

Confirmations

6,647,961

Merkle Root

7bb8a9c58ffb1279707027ffc7112d0126d25853e76f2229ed81f91cf07e7fda

Transactions (1)

Coinbase7bb8a9c58ffb12…81f91cf07e7fda

1 in → 1 out10.3200 XPM109 B

AMkTQyY4…oAfC2t1e

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.

4.026 × 10⁹²(93-digit number)

40269874769750412778…68360803608574957840

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

4.026 × 10⁹²(93-digit number)

40269874769750412778…68360803608574957839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.026 × 10⁹²(93-digit number)

40269874769750412778…68360803608574957841

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

8.053 × 10⁹²(93-digit number)

80539749539500825557…36721607217149915679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.053 × 10⁹²(93-digit number)

80539749539500825557…36721607217149915681

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

1.610 × 10⁹³(94-digit number)

16107949907900165111…73443214434299831359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.610 × 10⁹³(94-digit number)

16107949907900165111…73443214434299831361

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

3.221 × 10⁹³(94-digit number)

32215899815800330222…46886428868599662719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.221 × 10⁹³(94-digit number)

32215899815800330222…46886428868599662721

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

6.443 × 10⁹³(94-digit number)

64431799631600660445…93772857737199325439

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 143019

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 1a719a2e1f263dc9778cd1a85b47607e0cdafbb379e67c45f70381389d42f945

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 #143,019 on Chainz ↗