Home/Chain Registry/Block #2,138,250

Block #2,138,250

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/30/2017, 5:37:44 PM · Difficulty 10.8843 · 4,687,865 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b2d51d16dc05b30c97ddaa16dd61930f9edf16e28a1463992c8d24aaebf75fa2

View on Chainz ↗

Height

#2,138,250

Difficulty

10.884330

Transactions

Size

877 B

Version

Bits

0ae26379

Nonce

304,283,526

Timestamp

5/30/2017, 5:37:44 PM

Confirmations

4,687,865

Merkle Root

358affe32ac34edbedef1a1d3a917c524f8edac67e1139f93fd24699d3e5d5a2

Transactions (4)

Coinbase38ac802a91ed2c…28a4ff83ba3acb

1 in → 1 out8.4600 XPM110 B

Aem2fVUA…Qc1PoCiE

c16bdc45daf98d…daf1e65a17dec5

1 in → 2 out321.7105 XPM225 B

ATcox7cs…avCDunNu AH1bRhLz…qKGK7CQY

e1270caa4c602a…c706959679a13b

1 in → 2 out5.6441 XPM227 B

AUyCuGjK…ajKrKJpx APcBZdcu…7JfV25rX

a2ae9e49a6a90f…20c39cefa960b6

1 in → 2 out2.4575 XPM225 B

AQEVcn3y…YLvUmZQX ANwtSRNc…za9KnLoD

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.

7.143 × 10⁹⁴(95-digit number)

71433272753979229415…24155078214417246720

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

7.143 × 10⁹⁴(95-digit number)

71433272753979229415…24155078214417246719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.143 × 10⁹⁴(95-digit number)

71433272753979229415…24155078214417246721

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

1.428 × 10⁹⁵(96-digit number)

14286654550795845883…48310156428834493439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.428 × 10⁹⁵(96-digit number)

14286654550795845883…48310156428834493441

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

2.857 × 10⁹⁵(96-digit number)

28573309101591691766…96620312857668986879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.857 × 10⁹⁵(96-digit number)

28573309101591691766…96620312857668986881

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

5.714 × 10⁹⁵(96-digit number)

57146618203183383532…93240625715337973759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.714 × 10⁹⁵(96-digit number)

57146618203183383532…93240625715337973761

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

1.142 × 10⁹⁶(97-digit number)

11429323640636676706…86481251430675947519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.142 × 10⁹⁶(97-digit number)

11429323640636676706…86481251430675947521

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

2.285 × 10⁹⁶(97-digit number)

22858647281273353412…72962502861351895039

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 2138250

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 b2d51d16dc05b30c97ddaa16dd61930f9edf16e28a1463992c8d24aaebf75fa2

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 #2,138,250 on Chainz ↗

Block #2,138,250

Cookie Preferences