Home/Chain Registry/Block #2,634,180

Block #2,634,180

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 7:15:14 PM · Difficulty 11.2281 · 4,197,292 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b6792df581dfa54b4ba5dda921a5595a59ae7bd0e21c8355cdd2b346a8aa3921

View on Chainz ↗

Height

#2,634,180

Difficulty

11.228090

Transactions

Size

607 B

Version

Bits

0b3a6423

Nonce

64,890,249

Timestamp

4/28/2018, 7:15:14 PM

Confirmations

4,197,292

Merkle Root

e01e77065f534e2e18e86492dea28298eb56bbf335e72dba259935d898b9964d

Transactions (2)

Coinbase8d176ea1d68a19…ee4138c647bc92

1 in → 1 out7.9300 XPM109 B

AJsm8J4p…6dLmrNLV

e085eba72b624d…d86a92b95d423c

2 in → 3 out113.9870 XPM407 B

Aczhfikb…324c9DCs ATb6dfDH…sbxvGgQz AKDU4sfw…sXwTgU4p

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.

1.058 × 10⁹⁷(98-digit number)

10582255849361355035…73994026467750174720

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

1.058 × 10⁹⁷(98-digit number)

10582255849361355035…73994026467750174719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.058 × 10⁹⁷(98-digit number)

10582255849361355035…73994026467750174721

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

2.116 × 10⁹⁷(98-digit number)

21164511698722710071…47988052935500349439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.116 × 10⁹⁷(98-digit number)

21164511698722710071…47988052935500349441

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

4.232 × 10⁹⁷(98-digit number)

42329023397445420142…95976105871000698879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.232 × 10⁹⁷(98-digit number)

42329023397445420142…95976105871000698881

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

8.465 × 10⁹⁷(98-digit number)

84658046794890840284…91952211742001397759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.465 × 10⁹⁷(98-digit number)

84658046794890840284…91952211742001397761

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

1.693 × 10⁹⁸(99-digit number)

16931609358978168056…83904423484002795519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.693 × 10⁹⁸(99-digit number)

16931609358978168056…83904423484002795521

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

3.386 × 10⁹⁸(99-digit number)

33863218717956336113…67808846968005591039

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 2634180

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 b6792df581dfa54b4ba5dda921a5595a59ae7bd0e21c8355cdd2b346a8aa3921

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 #2,634,180 on Chainz ↗

Block #2,634,180

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