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Block #2,281,996

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/4/2017, 11:01:03 AM · Difficulty 10.9557 · 4,544,428 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eca56e264917d45c955feab92e3da5a6ad84ed81118c0d857269c55a4aa5872f

View on Chainz ↗

Height

#2,281,996

Difficulty

10.955678

Transactions

Size

1.36 KB

Version

Bits

0af4a748

Nonce

230,639,513

Timestamp

9/4/2017, 11:01:03 AM

Confirmations

4,544,428

Merkle Root

c7409d6779cbe33b8b4e5367dfc400a11f8112328f994f425e84379b1dc573d4

Transactions (3)

Coinbase0c375d281df90d…d0ad1a6fb4c2f0

1 in → 1 out8.3400 XPM109 B

AMZkWcqt…6QXf88qd

9aa192fa3396b0…dedf819494e9ae

2 in → 2 out3.1383 XPM374 B

AXCz3i15…bd3tZodd AGhStPUm…6aisYwLu

3db29becb9a7df…c0a412d98cfd17

5 in → 2 out1.0890 XPM817 B

ASzaZHfo…ri2ytYaC ARCFb9iC…HHVhgUv6

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.

3.325 × 10⁹⁴(95-digit number)

33257115304703166362…83123621167331091160

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

3.325 × 10⁹⁴(95-digit number)

33257115304703166362…83123621167331091159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.325 × 10⁹⁴(95-digit number)

33257115304703166362…83123621167331091161

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

6.651 × 10⁹⁴(95-digit number)

66514230609406332725…66247242334662182319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.651 × 10⁹⁴(95-digit number)

66514230609406332725…66247242334662182321

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

1.330 × 10⁹⁵(96-digit number)

13302846121881266545…32494484669324364639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.330 × 10⁹⁵(96-digit number)

13302846121881266545…32494484669324364641

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

2.660 × 10⁹⁵(96-digit number)

26605692243762533090…64988969338648729279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.660 × 10⁹⁵(96-digit number)

26605692243762533090…64988969338648729281

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

5.321 × 10⁹⁵(96-digit number)

53211384487525066180…29977938677297458559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.321 × 10⁹⁵(96-digit number)

53211384487525066180…29977938677297458561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 2281996

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 eca56e264917d45c955feab92e3da5a6ad84ed81118c0d857269c55a4aa5872f

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 #2,281,996 on Chainz ↗

Block #2,281,996

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