Home/Chain Registry/Block #2,283,570

Block #2,283,570

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/5/2017, 1:55:35 PM · Difficulty 10.9554 · 4,548,283 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2eef6ddd56b83471e447ed3b9bf21e277f0b94c5a05ec9228e9d7402e1c479c

View on Chainz ↗

Height

#2,283,570

Difficulty

10.955374

Transactions

Size

1.94 KB

Version

Bits

0af4936a

Nonce

105,052,261

Timestamp

9/5/2017, 1:55:35 PM

Confirmations

4,548,283

Merkle Root

ab63b871c74cabb3a2a62ca5e16203a3fa8386bda9cef476bef658bb29ff4059

Transactions (3)

Coinbasec853bbd6b587e6…84f7ee50b18f78

1 in → 1 out8.3400 XPM110 B

AGHDFiT3…TzYNTYaS

621d1010391e5a…cecadb2ec2e99c

6 in → 2 out2970.0125 XPM969 B

Aehfvdnf…MAoqvA8W AZhGstey…MLCpB71x

4e7c31961fda6a…d9f5c57a670261

5 in → 2 out2970.8267 XPM817 B

Aehfvdnf…MAoqvA8W AbtSkFwY…xuodswmN

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.

2.519 × 10⁹⁶(97-digit number)

25196374057638071305…56450354489573207040

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

2.519 × 10⁹⁶(97-digit number)

25196374057638071305…56450354489573207039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.519 × 10⁹⁶(97-digit number)

25196374057638071305…56450354489573207041

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

5.039 × 10⁹⁶(97-digit number)

50392748115276142610…12900708979146414079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.039 × 10⁹⁶(97-digit number)

50392748115276142610…12900708979146414081

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

1.007 × 10⁹⁷(98-digit number)

10078549623055228522…25801417958292828159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.007 × 10⁹⁷(98-digit number)

10078549623055228522…25801417958292828161

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

2.015 × 10⁹⁷(98-digit number)

20157099246110457044…51602835916585656319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.015 × 10⁹⁷(98-digit number)

20157099246110457044…51602835916585656321

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

4.031 × 10⁹⁷(98-digit number)

40314198492220914088…03205671833171312639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.031 × 10⁹⁷(98-digit number)

40314198492220914088…03205671833171312641

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 2283570

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 c2eef6ddd56b83471e447ed3b9bf21e277f0b94c5a05ec9228e9d7402e1c479c

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 #2,283,570 on Chainz ↗

Block #2,283,570

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