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Block #300,150

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 10:17:35 AM · Difficulty 9.9922 · 6,513,683 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2dbbd1433fe859edaf570130f909df07b2c4c80e56523b8a480d5cde16df4afe

View on Chainz ↗

Height

#300,150

Difficulty

9.992223

Transactions

Size

1.86 KB

Version

Bits

09fe0258

Nonce

113,249

Timestamp

12/8/2013, 10:17:35 AM

Confirmations

6,513,683

Merkle Root

fe0ff00be74313ef1f4205d1f12f90b52b49ae84dfb878536e577d4da3889aea

Transactions (4)

Coinbased02d4e36032c3e…60fd73a83b0b25

1 in → 1 out10.0000 XPM97 B

AWQBKr3Y…sUA1Ehpd

3e0873693f0c41…e01136983d3b93

1 in → 2 out3860.4490 XPM227 B

AHiqzUT7…gZ2zy4Dq AXiN5cd9…5VumZJEP

ecfda6f6d24213…75b60c13b1a5c8

8 in → 2 out2.0799 XPM1.23 KB

AHu1Yu6C…FLQepPGx AVts99YX…oSHDt3v4

a9ed13e00fbc85…0eff00839f1593

1 in → 2 out3859.3714 XPM225 B

AJdvJmjS…GFTusQmv AbZ4wWEW…UaxWweqd

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.

3.819 × 10⁹⁶(97-digit number)

38192274338827328979…33886246635466290560

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

3.819 × 10⁹⁶(97-digit number)

38192274338827328979…33886246635466290559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.819 × 10⁹⁶(97-digit number)

38192274338827328979…33886246635466290561

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

7.638 × 10⁹⁶(97-digit number)

76384548677654657958…67772493270932581119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.638 × 10⁹⁶(97-digit number)

76384548677654657958…67772493270932581121

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

1.527 × 10⁹⁷(98-digit number)

15276909735530931591…35544986541865162239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.527 × 10⁹⁷(98-digit number)

15276909735530931591…35544986541865162241

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

3.055 × 10⁹⁷(98-digit number)

30553819471061863183…71089973083730324479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.055 × 10⁹⁷(98-digit number)

30553819471061863183…71089973083730324481

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

6.110 × 10⁹⁷(98-digit number)

61107638942123726367…42179946167460648959

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 300150

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 2dbbd1433fe859edaf570130f909df07b2c4c80e56523b8a480d5cde16df4afe

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 #300,150 on Chainz ↗

Block #300,150

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