Home/Chain Registry/Block #362,907

Block #362,907

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/17/2014, 12:57:54 AM · Difficulty 10.4161 · 6,449,255 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9b812beca842d022044b2a11a74da94386a8a830f4958953c3e3dabc5986507f

View on Chainz ↗

Height

#362,907

Difficulty

10.416135

Transactions

Size

209 B

Version

Bits

0a6a87cb

Nonce

617

Timestamp

1/17/2014, 12:57:54 AM

Confirmations

6,449,255

Merkle Root

3b4c253c5cd5670b4b50fbf4937dbf94ea189eb1e95c3b17c64b92acd6cea728

Transactions (1)

Coinbase3b4c253c5cd567…4b92acd6cea728

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

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.

2.169 × 10¹⁰²(103-digit number)

21691201829869454452…56891669628971909120

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

2.169 × 10¹⁰²(103-digit number)

21691201829869454452…56891669628971909119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.169 × 10¹⁰²(103-digit number)

21691201829869454452…56891669628971909121

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

4.338 × 10¹⁰²(103-digit number)

43382403659738908905…13783339257943818239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.338 × 10¹⁰²(103-digit number)

43382403659738908905…13783339257943818241

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

8.676 × 10¹⁰²(103-digit number)

86764807319477817810…27566678515887636479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.676 × 10¹⁰²(103-digit number)

86764807319477817810…27566678515887636481

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

1.735 × 10¹⁰³(104-digit number)

17352961463895563562…55133357031775272959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.735 × 10¹⁰³(104-digit number)

17352961463895563562…55133357031775272961

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

3.470 × 10¹⁰³(104-digit number)

34705922927791127124…10266714063550545919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.470 × 10¹⁰³(104-digit number)

34705922927791127124…10266714063550545921

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 362907

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 9b812beca842d022044b2a11a74da94386a8a830f4958953c3e3dabc5986507f

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 #362,907 on Chainz ↗

Block #362,907

Cookie Preferences