Home/Chain Registry/Block #145,017

Block #145,017

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/1/2013, 3:48:58 PM · Difficulty 9.8420 · 6,646,430 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0830de157b80e0dbff13b07ccd8017108526793e0094af1365852c0b5d397efa

View on Chainz ↗

Height

#145,017

Difficulty

9.842014

Transactions

Size

198 B

Version

Bits

09d78e43

Nonce

175,443

Timestamp

9/1/2013, 3:48:58 PM

Confirmations

6,646,430

Merkle Root

a24790203c08f0443ee40bb2f98c31bb7b3978448fc9bb7166e2a11f6923abf2

Transactions (1)

Coinbasea24790203c08f0…e2a11f6923abf2

1 in → 1 out10.3100 XPM109 B

AG9Sgj9g…iSbfWnNU

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.

1.169 × 10⁹²(93-digit number)

11696103827461399847…17008178430298441120

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

1.169 × 10⁹²(93-digit number)

11696103827461399847…17008178430298441119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.169 × 10⁹²(93-digit number)

11696103827461399847…17008178430298441121

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

2.339 × 10⁹²(93-digit number)

23392207654922799694…34016356860596882239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.339 × 10⁹²(93-digit number)

23392207654922799694…34016356860596882241

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

4.678 × 10⁹²(93-digit number)

46784415309845599388…68032713721193764479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.678 × 10⁹²(93-digit number)

46784415309845599388…68032713721193764481

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

9.356 × 10⁹²(93-digit number)

93568830619691198776…36065427442387528959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.356 × 10⁹²(93-digit number)

93568830619691198776…36065427442387528961

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

1.871 × 10⁹³(94-digit number)

18713766123938239755…72130854884775057919

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 145017

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 0830de157b80e0dbff13b07ccd8017108526793e0094af1365852c0b5d397efa

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 #145,017 on Chainz ↗