Home/Chain Registry/Block #2,641,122

Block #2,641,122

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 6:04:21 AM · Difficulty 11.6079 · 4,189,653 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

419c0ebbb605b4ea4636eb8292867adb61286766504e71475f0f5b63af4abba8

View on Chainz ↗

Height

#2,641,122

Difficulty

11.607933

Transactions

Size

1.36 KB

Version

Bits

0b9ba17c

Nonce

105,318,067

Timestamp

5/1/2018, 6:04:21 AM

Confirmations

4,189,653

Merkle Root

56adff3f40e876f2b97115ced5100d2472a3f741784463557089079e53425684

Transactions (3)

Coinbaseb137b6ee1852ca…ba6dcabd6b63e1

1 in → 1 out7.4300 XPM110 B

AXhM7fgb…Lco4rW9S

63504266f2b343…f7b46c2519e096

1 in → 2 out1205.9500 XPM226 B

AHXjZNKW…L7fdyqqR ARJQLHRp…K8XqtAkd

9265bd293cb59c…6c14102bb796fd

6 in → 2 out31.5774 XPM967 B

AXAkV1i8…bi9Vo525 AZ4UnHzJ…PH7NQioA

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.

7.741 × 10⁹⁷(98-digit number)

77418257452248625525…73174307607328358400

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

7.741 × 10⁹⁷(98-digit number)

77418257452248625525…73174307607328358399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.741 × 10⁹⁷(98-digit number)

77418257452248625525…73174307607328358401

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

1.548 × 10⁹⁸(99-digit number)

15483651490449725105…46348615214656716799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.548 × 10⁹⁸(99-digit number)

15483651490449725105…46348615214656716801

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

3.096 × 10⁹⁸(99-digit number)

30967302980899450210…92697230429313433599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.096 × 10⁹⁸(99-digit number)

30967302980899450210…92697230429313433601

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

6.193 × 10⁹⁸(99-digit number)

61934605961798900420…85394460858626867199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.193 × 10⁹⁸(99-digit number)

61934605961798900420…85394460858626867201

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

1.238 × 10⁹⁹(100-digit number)

12386921192359780084…70788921717253734399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.238 × 10⁹⁹(100-digit number)

12386921192359780084…70788921717253734401

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

2.477 × 10⁹⁹(100-digit number)

24773842384719560168…41577843434507468799

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 2641122

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 419c0ebbb605b4ea4636eb8292867adb61286766504e71475f0f5b63af4abba8

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 #2,641,122 on Chainz ↗

Block #2,641,122

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