Home/Chain Registry/Block #2,838,108

Block #2,838,108

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/13/2018, 11:19:39 PM · Difficulty 11.7177 · 4,003,469 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

30aab3a1c4eec99350b13def710d4a56b4a7d4e68452fe89d47d597bef97e382

View on Chainz ↗

Height

#2,838,108

Difficulty

11.717706

Transactions

Size

1.07 KB

Version

Bits

0bb7bb93

Nonce

498,245,040

Timestamp

9/13/2018, 11:19:39 PM

Confirmations

4,003,469

Merkle Root

579db5b5d1c551f198cae2ea0d2d43bd9104e6c0fe3214f123cf3afc46e1d6c7

Transactions (3)

Coinbase7a60f144cf8fb2…a21c6725d46d61

1 in → 1 out7.2900 XPM110 B

AHVP8kq1…YoKhNzMH

e391da41c12a16…75bc8a96247458

2 in → 2 out4.3100 XPM373 B

AQCvpZ5h…ZYqBbcZh AZiXxXty…AFv43CYF

dacc4bc83fd3eb…e7dad4f213ab02

3 in → 2 out4.0600 XPM525 B

ASMzJrhv…T1pDSw8e AdDL5zHF…1E8yFum8

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.

3.184 × 10⁹⁷(98-digit number)

31841458594545363595…17211020201631500800

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

3.184 × 10⁹⁷(98-digit number)

31841458594545363595…17211020201631500799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.184 × 10⁹⁷(98-digit number)

31841458594545363595…17211020201631500801

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

6.368 × 10⁹⁷(98-digit number)

63682917189090727190…34422040403263001599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.368 × 10⁹⁷(98-digit number)

63682917189090727190…34422040403263001601

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

1.273 × 10⁹⁸(99-digit number)

12736583437818145438…68844080806526003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.273 × 10⁹⁸(99-digit number)

12736583437818145438…68844080806526003201

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

2.547 × 10⁹⁸(99-digit number)

25473166875636290876…37688161613052006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.547 × 10⁹⁸(99-digit number)

25473166875636290876…37688161613052006401

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

5.094 × 10⁹⁸(99-digit number)

50946333751272581752…75376323226104012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.094 × 10⁹⁸(99-digit number)

50946333751272581752…75376323226104012801

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

1.018 × 10⁹⁹(100-digit number)

10189266750254516350…50752646452208025599

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 2838108

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 30aab3a1c4eec99350b13def710d4a56b4a7d4e68452fe89d47d597bef97e382

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 #2,838,108 on Chainz ↗

Block #2,838,108

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