Home/Chain Registry/Block #2,925,059

Block #2,925,059

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/16/2018, 6:32:18 AM · Difficulty 11.3559 · 3,915,559 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8f2211e409aa1573d0abfb20c9411bf5545b0ad09fcfcd84c19874ea02c2bab7

View on Chainz ↗

Height

#2,925,059

Difficulty

11.355856

Transactions

Size

1019 B

Version

Bits

0b5b1967

Nonce

513,964,556

Timestamp

11/16/2018, 6:32:18 AM

Confirmations

3,915,559

Merkle Root

3986ae8774ad036b27250ed5a1d317f63c5ed259a2e903c2a45e9738b0441c64

Transactions (2)

Coinbased0562f33fd87d8…c7daf5dc2fd49f

1 in → 1 out7.7500 XPM110 B

AUhjokok…k5m93PZR

7976cd2e7efb5f…deb769fb4923cf

5 in → 2 out5.2460 XPM818 B

AbXwmGxD…4XXYP765 AZtM1QsL…JugreUPy

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.

4.072 × 10⁹⁷(98-digit number)

40722772535116011751…96603266230906201600

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

4.072 × 10⁹⁷(98-digit number)

40722772535116011751…96603266230906201599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.072 × 10⁹⁷(98-digit number)

40722772535116011751…96603266230906201601

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

8.144 × 10⁹⁷(98-digit number)

81445545070232023502…93206532461812403199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.144 × 10⁹⁷(98-digit number)

81445545070232023502…93206532461812403201

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

1.628 × 10⁹⁸(99-digit number)

16289109014046404700…86413064923624806399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.628 × 10⁹⁸(99-digit number)

16289109014046404700…86413064923624806401

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

3.257 × 10⁹⁸(99-digit number)

32578218028092809401…72826129847249612799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.257 × 10⁹⁸(99-digit number)

32578218028092809401…72826129847249612801

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

6.515 × 10⁹⁸(99-digit number)

65156436056185618802…45652259694499225599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.515 × 10⁹⁸(99-digit number)

65156436056185618802…45652259694499225601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.303 × 10⁹⁹(100-digit number)

13031287211237123760…91304519388998451199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 2925059

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 8f2211e409aa1573d0abfb20c9411bf5545b0ad09fcfcd84c19874ea02c2bab7

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 #2,925,059 on Chainz ↗

Block #2,925,059

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