Home/Chain Registry/Block #2,730,132

Block #2,730,132

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/1/2018, 9:34:05 PM · Difficulty 11.6297 · 4,115,002 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

14398673addd65288152d1aec248f035dda4e9df235d20cdc6246bbe02ebae29

View on Chainz ↗

Height

#2,730,132

Difficulty

11.629739

Transactions

Size

914 B

Version

Bits

0ba13696

Nonce

314,726,987

Timestamp

7/1/2018, 9:34:05 PM

Confirmations

4,115,002

Merkle Root

e3fdb64265ac1fb65d558031b3694643ecfb7fea82c56bcd61350bfc56a37de6

Transactions (3)

Coinbase09cf717562814d…70002da18bcae7

1 in → 1 out7.4000 XPM110 B

AaGabTAy…o6yqt6tg

f4e4e3dc29f34a…f1e193c4ab21ce

2 in → 2 out12.2700 XPM340 B

ARqi3jyP…bBbDHVxX ALrsRZGv…7VzvvnV1

f96a41c02db217…6ee3452797a418

2 in → 2 out4.2700 XPM374 B

AeLHLxcd…r4W7rpgo AaPiKjSS…KfA5HLTT

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.

2.800 × 10⁹⁴(95-digit number)

28009051856460502271…91260835531010570080

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

2.800 × 10⁹⁴(95-digit number)

28009051856460502271…91260835531010570079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.800 × 10⁹⁴(95-digit number)

28009051856460502271…91260835531010570081

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

5.601 × 10⁹⁴(95-digit number)

56018103712921004542…82521671062021140159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.601 × 10⁹⁴(95-digit number)

56018103712921004542…82521671062021140161

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

1.120 × 10⁹⁵(96-digit number)

11203620742584200908…65043342124042280319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.120 × 10⁹⁵(96-digit number)

11203620742584200908…65043342124042280321

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

2.240 × 10⁹⁵(96-digit number)

22407241485168401816…30086684248084560639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.240 × 10⁹⁵(96-digit number)

22407241485168401816…30086684248084560641

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

4.481 × 10⁹⁵(96-digit number)

44814482970336803633…60173368496169121279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.481 × 10⁹⁵(96-digit number)

44814482970336803633…60173368496169121281

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

8.962 × 10⁹⁵(96-digit number)

89628965940673607267…20346736992338242559

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 2730132

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 14398673addd65288152d1aec248f035dda4e9df235d20cdc6246bbe02ebae29

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 #2,730,132 on Chainz ↗

Block #2,730,132

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