Home/Chain Registry/Block #270,165

Block #270,165

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 6:13:23 PM · Difficulty 9.9518 · 6,521,748 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1629ecffb839ed9a933fd9229660efdf80d9a91fd923f882082e6d15feaaa62c

View on Chainz ↗

Height

#270,165

Difficulty

9.951811

Transactions

Size

205 B

Version

Bits

09f3a9e6

Nonce

28,138

Timestamp

11/23/2013, 6:13:23 PM

Confirmations

6,521,748

Merkle Root

e9868299084c0562d5c196aab55b4ef7596bab92f964a9a77d143133a1b5dce1

Transactions (1)

Coinbasee9868299084c05…143133a1b5dce1

1 in → 1 out10.0800 XPM116 B

AcLBm5Z9…S683d7c3

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.

2.105 × 10⁹²(93-digit number)

21052276322593986391…97662779086680686530

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

2.105 × 10⁹²(93-digit number)

21052276322593986391…97662779086680686529

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.105 × 10⁹²(93-digit number)

21052276322593986391…97662779086680686531

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

4.210 × 10⁹²(93-digit number)

42104552645187972782…95325558173361373059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.210 × 10⁹²(93-digit number)

42104552645187972782…95325558173361373061

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

8.420 × 10⁹²(93-digit number)

84209105290375945565…90651116346722746119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.420 × 10⁹²(93-digit number)

84209105290375945565…90651116346722746121

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

1.684 × 10⁹³(94-digit number)

16841821058075189113…81302232693445492239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.684 × 10⁹³(94-digit number)

16841821058075189113…81302232693445492241

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

3.368 × 10⁹³(94-digit number)

33683642116150378226…62604465386890984479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.368 × 10⁹³(94-digit number)

33683642116150378226…62604465386890984481

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 270165

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 1629ecffb839ed9a933fd9229660efdf80d9a91fd923f882082e6d15feaaa62c

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 #270,165 on Chainz ↗