Home/Chain Registry/Block #268,439

Block #268,439

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 3:29:46 AM · Difficulty 9.9571 · 6,558,079 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8288abb15d3e51818963f42ba8aad120b166a53c4cf029cd3172cd75e91223d6

View on Chainz ↗

Height

#268,439

Difficulty

9.957121

Transactions

Size

1.94 KB

Version

Bits

09f505e3

Nonce

77,678

Timestamp

11/22/2013, 3:29:46 AM

Confirmations

6,558,079

Merkle Root

d88279e95c6396f506da9216f71963c452da44feb56148a06d826a3909926eed

Transactions (3)

Coinbase12dd477b185e55…3217b1d20e7948

1 in → 1 out10.1000 XPM109 B

APp8gMBs…uhi9yykC

5d84a7155f7795…359b988276c322

5 in → 2 out15005.4928 XPM819 B

AR5Um3BU…fvkkRpsy ALKwE6HX…N1yXR7L1

63e34513b3e135…8a1e6dbf61643a

6 in → 2 out2138.0100 XPM967 B

AL4VkdtF…5sgr8gup AVRTQRyU…g5hWyN8R

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.

1.848 × 10⁹⁴(95-digit number)

18484633391119978299…46916513746887064320

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

1.848 × 10⁹⁴(95-digit number)

18484633391119978299…46916513746887064319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.848 × 10⁹⁴(95-digit number)

18484633391119978299…46916513746887064321

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

3.696 × 10⁹⁴(95-digit number)

36969266782239956599…93833027493774128639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.696 × 10⁹⁴(95-digit number)

36969266782239956599…93833027493774128641

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

7.393 × 10⁹⁴(95-digit number)

73938533564479913198…87666054987548257279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.393 × 10⁹⁴(95-digit number)

73938533564479913198…87666054987548257281

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

1.478 × 10⁹⁵(96-digit number)

14787706712895982639…75332109975096514559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.478 × 10⁹⁵(96-digit number)

14787706712895982639…75332109975096514561

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

2.957 × 10⁹⁵(96-digit number)

29575413425791965279…50664219950193029119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 268439

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 8288abb15d3e51818963f42ba8aad120b166a53c4cf029cd3172cd75e91223d6

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 #268,439 on Chainz ↗

Block #268,439

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