Home/Chain Registry/Block #303,651

Block #303,651

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 12:10:09 PM · Difficulty 9.9931 · 6,513,969 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3530dedfbab603f7605f0b236f1c3c5a415a918aab1c8fa8c6fb4d5f77e6d32c

View on Chainz ↗

Height

#303,651

Difficulty

9.993074

Transactions

Size

1.05 KB

Version

Bits

09fe3a15

Nonce

958

Timestamp

12/10/2013, 12:10:09 PM

Confirmations

6,513,969

Merkle Root

b6a06ca1d3288cba82bff29748986a16ad2461e4f7c4d592439a83d2ed061ab4

Transactions (1)

Coinbaseb6a06ca1d3288c…9a83d2ed061ab4

1 in → 27 out10.0000 XPM981 B

AHuJ9wYh…BGmgHrKZ Ad9pSzHt…cpJ3y2zz AZ2pPuKg…95SN2Yr7 ARcqMJhp…RVLToQ6S AG5YAjec…VhA4Aeh1

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.

1.227 × 10⁹⁷(98-digit number)

12272533649414704912…38851517527149844480

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

1.227 × 10⁹⁷(98-digit number)

12272533649414704912…38851517527149844479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.227 × 10⁹⁷(98-digit number)

12272533649414704912…38851517527149844481

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

2.454 × 10⁹⁷(98-digit number)

24545067298829409824…77703035054299688959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.454 × 10⁹⁷(98-digit number)

24545067298829409824…77703035054299688961

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

4.909 × 10⁹⁷(98-digit number)

49090134597658819649…55406070108599377919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.909 × 10⁹⁷(98-digit number)

49090134597658819649…55406070108599377921

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

9.818 × 10⁹⁷(98-digit number)

98180269195317639298…10812140217198755839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.818 × 10⁹⁷(98-digit number)

98180269195317639298…10812140217198755841

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

1.963 × 10⁹⁸(99-digit number)

19636053839063527859…21624280434397511679

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 303651

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 3530dedfbab603f7605f0b236f1c3c5a415a918aab1c8fa8c6fb4d5f77e6d32c

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 #303,651 on Chainz ↗

Block #303,651

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