Home/Chain Registry/Block #172,489

Block #172,489

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/20/2013, 7:16:16 AM · Difficulty 9.8618 · 6,652,161 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9265960911160080fe1ef914d5eedca72b6042457b47b0282baea1e259ffd6af

View on Chainz ↗

Height

#172,489

Difficulty

9.861803

Transactions

Size

2.53 KB

Version

Bits

09dc9f21

Nonce

3,435

Timestamp

9/20/2013, 7:16:16 AM

Confirmations

6,652,161

Merkle Root

1f874b62e1f295495277b8810994def0d9c5ebb3eba267ffff1f26af43b9a3df

Transactions (4)

Coinbaseb25ccc97a8b8ca…d67a567e2533f5

1 in → 1 out10.3100 XPM109 B

AYKFccHZ…CdXZ542n

dd99810b4fddc1…8cca009525461d

4 in → 2 out41.0200 XPM535 B

Ad7KGhDM…tbeRBJZY ARyYtqtL…uCP66s1P

133169ee734d85…e9c44325d8097a

1 in → 2 out8.1406 XPM226 B

AcADmAoe…8iNnoMzB AbxvKyky…ddt1CbuK

162e3339534071…b35ea3c925abd7

10 in → 4 out9.9352 XPM1.59 KB

ANxERLYc…v7fC1vqc ASNGcBGv…ezfPcGR1 AL7194fk…YNQBVjTB Ac5sZcdP…kzV4eckG

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.

2.240 × 10⁹⁵(96-digit number)

22401077638884968690…30307267807816625000

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

2.240 × 10⁹⁵(96-digit number)

22401077638884968690…30307267807816624999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.240 × 10⁹⁵(96-digit number)

22401077638884968690…30307267807816625001

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

4.480 × 10⁹⁵(96-digit number)

44802155277769937381…60614535615633249999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.480 × 10⁹⁵(96-digit number)

44802155277769937381…60614535615633250001

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

8.960 × 10⁹⁵(96-digit number)

89604310555539874762…21229071231266499999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.960 × 10⁹⁵(96-digit number)

89604310555539874762…21229071231266500001

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

1.792 × 10⁹⁶(97-digit number)

17920862111107974952…42458142462532999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.792 × 10⁹⁶(97-digit number)

17920862111107974952…42458142462533000001

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

3.584 × 10⁹⁶(97-digit number)

35841724222215949904…84916284925065999999

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 172489

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 9265960911160080fe1ef914d5eedca72b6042457b47b0282baea1e259ffd6af

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 #172,489 on Chainz ↗

Block #172,489

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