Home/Chain Registry/Block #2,795,287

Block #2,795,287

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/15/2018, 3:51:40 PM · Difficulty 11.6797 · 4,049,252 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0fbbfa9e5904388da56dcf2be722aa50d37516f5ede2e7f074ffe20672d070d

View on Chainz ↗

Height

#2,795,287

Difficulty

11.679678

Transactions

Size

427 B

Version

Bits

0badff5a

Nonce

993,374,640

Timestamp

8/15/2018, 3:51:40 PM

Confirmations

4,049,252

Merkle Root

b3d1c17fa76197c1805a1ea992b50f2fd8032ce29662885686140dfc680366ef

Transactions (2)

Coinbase935de7f58ab446…d9fcef508dccf0

1 in → 1 out7.3300 XPM110 B

AMcidgaw…sAczshgU

f41ed0101a95aa…d1187931b9e77d

1 in → 2 out13289.8985 XPM226 B

AZZ4saM7…1mSewDQV ATLw4wqX…kGTEjXFm

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.

9.494 × 10⁹⁷(98-digit number)

94944918437951129234…29184564135748403200

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

9.494 × 10⁹⁷(98-digit number)

94944918437951129234…29184564135748403199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.494 × 10⁹⁷(98-digit number)

94944918437951129234…29184564135748403201

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

1.898 × 10⁹⁸(99-digit number)

18988983687590225846…58369128271496806399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.898 × 10⁹⁸(99-digit number)

18988983687590225846…58369128271496806401

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

3.797 × 10⁹⁸(99-digit number)

37977967375180451693…16738256542993612799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.797 × 10⁹⁸(99-digit number)

37977967375180451693…16738256542993612801

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

7.595 × 10⁹⁸(99-digit number)

75955934750360903387…33476513085987225599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.595 × 10⁹⁸(99-digit number)

75955934750360903387…33476513085987225601

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

1.519 × 10⁹⁹(100-digit number)

15191186950072180677…66953026171974451199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.519 × 10⁹⁹(100-digit number)

15191186950072180677…66953026171974451201

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

3.038 × 10⁹⁹(100-digit number)

30382373900144361355…33906052343948902399

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 2795287

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 b0fbbfa9e5904388da56dcf2be722aa50d37516f5ede2e7f074ffe20672d070d

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 #2,795,287 on Chainz ↗

Block #2,795,287

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