Home/Chain Registry/Block #2,640,755

Block #2,640,755

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 2:52:16 AM · Difficulty 11.5940 · 4,201,332 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e1b6f03c5e33e87aa8db9a98642bb902dc2df0758990499b7925b021a151c96a

View on Chainz ↗

Height

#2,640,755

Difficulty

11.594039

Transactions

Size

1.16 KB

Version

Bits

0b9812eb

Nonce

379,914,481

Timestamp

5/1/2018, 2:52:16 AM

Confirmations

4,201,332

Merkle Root

a255597e485ac760c5535bacecce40745659911cea40c5598a9eeefc8711d001

Transactions (4)

Coinbase918f6473004ca3…214b8d699e68f2

1 in → 1 out7.4600 XPM110 B

Adqah8zh…1WwoHJ9t

f08e6af3c6dc0c…198ceb7e0dacbe

2 in → 2 out15.2300 XPM306 B

AZRwXqE1…quNaokqE AaxPDp4S…dvVMSWnf

a583cc5803d455…6a66cb02c8b745

2 in → 2 out10.4900 XPM340 B

AXs8oSh1…1FvY4sbG ANw7sjd4…XL12izFi

0c7dfb9f27efff…335663acb67f96

2 in → 2 out12.8700 XPM342 B

ATw5qfr6…zwRHzQBb ANdAwc8j…tv1H16Px

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.

1.605 × 10⁹⁵(96-digit number)

16054139335667420796…21697277010654726400

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

1.605 × 10⁹⁵(96-digit number)

16054139335667420796…21697277010654726399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.605 × 10⁹⁵(96-digit number)

16054139335667420796…21697277010654726401

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

3.210 × 10⁹⁵(96-digit number)

32108278671334841593…43394554021309452799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.210 × 10⁹⁵(96-digit number)

32108278671334841593…43394554021309452801

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

6.421 × 10⁹⁵(96-digit number)

64216557342669683186…86789108042618905599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.421 × 10⁹⁵(96-digit number)

64216557342669683186…86789108042618905601

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

1.284 × 10⁹⁶(97-digit number)

12843311468533936637…73578216085237811199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.284 × 10⁹⁶(97-digit number)

12843311468533936637…73578216085237811201

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

2.568 × 10⁹⁶(97-digit number)

25686622937067873274…47156432170475622399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.568 × 10⁹⁶(97-digit number)

25686622937067873274…47156432170475622401

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

5.137 × 10⁹⁶(97-digit number)

51373245874135746549…94312864340951244799

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 2640755

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 e1b6f03c5e33e87aa8db9a98642bb902dc2df0758990499b7925b021a151c96a

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 #2,640,755 on Chainz ↗

Block #2,640,755

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