Home/Chain Registry/Block #2,271,144

Block #2,271,144

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/28/2017, 1:41:31 AM · Difficulty 10.9534 · 4,559,861 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1286dd197c96fc366b73cb1991359620b28421f7f9b36ea6e04658b30013c4a8

View on Chainz ↗

Height

#2,271,144

Difficulty

10.953449

Transactions

Size

2.01 KB

Version

Bits

0af41544

Nonce

352,220,401

Timestamp

8/28/2017, 1:41:31 AM

Confirmations

4,559,861

Merkle Root

316999049cba75778c4c689aea7fe0e80153644338e1cdd1189370f90d691d77

Transactions (4)

Coinbasea3c2b9fef3f97a…81bd0d275acb63

1 in → 1 out8.3500 XPM109 B

AZyHarWo…hrSok6JD

7468f962e99397…66ae2aac9cfc10

2 in → 2 out2147.1492 XPM375 B

Ac5xLb5b…nq8vi7AX AU7xkW52…RMPvkSaU

63657276691f63…ebb40ccd94bd6c

4 in → 2 out2274.0537 XPM670 B

AU59YY1q…N33rDqPj AJJbRMsG…RLz1VGF9

087d4f74a9b6ef…52e8a32b2b7f17

5 in → 2 out1187.3400 XPM819 B

ALuDXiBD…nzeBMYHr AU59YY1q…N33rDqPj

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.

8.447 × 10⁹³(94-digit number)

84479552858151985319…64041829232827707930

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

8.447 × 10⁹³(94-digit number)

84479552858151985319…64041829232827707929

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.447 × 10⁹³(94-digit number)

84479552858151985319…64041829232827707931

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

1.689 × 10⁹⁴(95-digit number)

16895910571630397063…28083658465655415859

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.689 × 10⁹⁴(95-digit number)

16895910571630397063…28083658465655415861

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

3.379 × 10⁹⁴(95-digit number)

33791821143260794127…56167316931310831719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.379 × 10⁹⁴(95-digit number)

33791821143260794127…56167316931310831721

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

6.758 × 10⁹⁴(95-digit number)

67583642286521588255…12334633862621663439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.758 × 10⁹⁴(95-digit number)

67583642286521588255…12334633862621663441

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

1.351 × 10⁹⁵(96-digit number)

13516728457304317651…24669267725243326879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.351 × 10⁹⁵(96-digit number)

13516728457304317651…24669267725243326881

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 2271144

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 1286dd197c96fc366b73cb1991359620b28421f7f9b36ea6e04658b30013c4a8

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 #2,271,144 on Chainz ↗

Block #2,271,144

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