Home/Chain Registry/Block #2,632,834

Block #2,632,834

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 2:08:17 AM · Difficulty 11.1776 · 4,209,565 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e38f52d28bd9aa77f989866b2293678fedc9a2f293f0496af7837e184f45293d

View on Chainz ↗

Height

#2,632,834

Difficulty

11.177576

Transactions

Size

1.19 KB

Version

Bits

0b2d759f

Nonce

104,955,407

Timestamp

4/28/2018, 2:08:17 AM

Confirmations

4,209,565

Merkle Root

eed52b9cabb2909012f5657506d0e1ded801247484019eea4ce197d90f72b5e5

Transactions (4)

Coinbasebb14aa0f539ede…7e6a0067cc863d

1 in → 1 out8.0200 XPM109 B

Adqah8zh…1WwoHJ9t

3475fd17932847…c16488e947fddd

2 in → 2 out16.0700 XPM304 B

AM6XD26m…RcphfPC1 ANeLnz7A…LnPTAf3M

edb70a5b2ade83…2e0d99570d193f

2 in → 2 out13.9500 XPM340 B

AZmCsR6r…pREZNmet ASiP8JeT…FBf3SDBU

11d7653a3e8ed0…b23c3cad7e46ba

2 in → 2 out10.0100 XPM374 B

AG29rrpH…pKWogpwr Aei7Ymdr…MjKXcgCp

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.

1.263 × 10⁹⁸(99-digit number)

12637007771265339958…84029070587266007040

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

1.263 × 10⁹⁸(99-digit number)

12637007771265339958…84029070587266007039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.263 × 10⁹⁸(99-digit number)

12637007771265339958…84029070587266007041

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

2.527 × 10⁹⁸(99-digit number)

25274015542530679916…68058141174532014079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.527 × 10⁹⁸(99-digit number)

25274015542530679916…68058141174532014081

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

5.054 × 10⁹⁸(99-digit number)

50548031085061359832…36116282349064028159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.054 × 10⁹⁸(99-digit number)

50548031085061359832…36116282349064028161

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

1.010 × 10⁹⁹(100-digit number)

10109606217012271966…72232564698128056319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.010 × 10⁹⁹(100-digit number)

10109606217012271966…72232564698128056321

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

2.021 × 10⁹⁹(100-digit number)

20219212434024543933…44465129396256112639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.021 × 10⁹⁹(100-digit number)

20219212434024543933…44465129396256112641

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

4.043 × 10⁹⁹(100-digit number)

40438424868049087866…88930258792512225279

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 2632834

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 e38f52d28bd9aa77f989866b2293678fedc9a2f293f0496af7837e184f45293d

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 #2,632,834 on Chainz ↗

Block #2,632,834

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