Home/Chain Registry/Block #2,810,287

Block #2,810,287

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 8/26/2018, 5:09:23 AM · Difficulty 11.6673 · 4,029,101 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bc78bf8bbc3ac5e1ba3ea9e8a314fd905fcefbcc100071ad0d44053ec66fa4b8

View on Chainz ↗

Height

#2,810,287

Difficulty

11.667328

Transactions

Size

1.29 KB

Version

Bits

0baad5ff

Nonce

1,417,818,827

Timestamp

8/26/2018, 5:09:23 AM

Confirmations

4,029,101

Merkle Root

501b8c13442efc93b7e87ffb5e7f262bf40b140e96df1f96b2e3bc4761cf1265

Transactions (4)

Coinbase0e211d3fd7beea…5dd3da270ff4f9

1 in → 1 out7.3600 XPM110 B

AZtxQr2F…7grUWrUz

90532773a2569c…ce660671686061

2 in → 2 out5.9500 XPM374 B

AN83v1TU…kcXerDsJ ARsRHsB9…KG7kbs5Q

016b5c1c34172c…be323bb2889dce

2 in → 2 out5.9400 XPM374 B

AMLiyYLv…iYQLf2JU AWYpuwTx…QDkMHV51

88498edfac1d57…a8485dfdb8feae

2 in → 2 out5.9500 XPM375 B

ASuZtLHV…8RGMsM7i ANW586i4…NZyxEBvd

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.

9.249 × 10⁹⁶(97-digit number)

92490272272665011577…24804472743476858880

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

9.249 × 10⁹⁶(97-digit number)

92490272272665011577…24804472743476858879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.249 × 10⁹⁶(97-digit number)

92490272272665011577…24804472743476858881

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

1.849 × 10⁹⁷(98-digit number)

18498054454533002315…49608945486953717759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.849 × 10⁹⁷(98-digit number)

18498054454533002315…49608945486953717761

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

3.699 × 10⁹⁷(98-digit number)

36996108909066004630…99217890973907435519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.699 × 10⁹⁷(98-digit number)

36996108909066004630…99217890973907435521

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

7.399 × 10⁹⁷(98-digit number)

73992217818132009261…98435781947814871039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.399 × 10⁹⁷(98-digit number)

73992217818132009261…98435781947814871041

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

1.479 × 10⁹⁸(99-digit number)

14798443563626401852…96871563895629742079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.479 × 10⁹⁸(99-digit number)

14798443563626401852…96871563895629742081

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

2.959 × 10⁹⁸(99-digit number)

29596887127252803704…93743127791259484159

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

2.959 × 10⁹⁸(99-digit number)

29596887127252803704…93743127791259484161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

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 2810287

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 bc78bf8bbc3ac5e1ba3ea9e8a314fd905fcefbcc100071ad0d44053ec66fa4b8

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 #2,810,287 on Chainz ↗

Block #2,810,287

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