Block #364,360

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2014, 12:33:52 AM · Difficulty 10.4216 · 6,427,620 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8606539f04ab84e8dff60b5da97a246e0fbdd57228a04db9fc7ccbbc9a36db3c

View on Chainz ↗

Height

#364,360

Difficulty

10.421600

Transactions

Size

1.09 KB

Version

Bits

0a6bedf6

Nonce

592

Timestamp

1/18/2014, 12:33:52 AM

Confirmations

6,427,620

Merkle Root

221a6ccda26debe1f67259bc5b26de5f96fb2fe90d1a28c1a7ca50b5123a6603

Transactions (5)

Coinbase5aea0e55e01df4…770e48c5c80945

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

c6c087513913ac…6a603560847a58

1 in → 2 out9.2100 XPM226 B

AMaFDmxv…Ncfnt9H3 ANBewaDF…xbSGTwqU

836b8e93bac31a…6a7c8313b289b7

1 in → 2 out8.1877 XPM226 B

AR1zWWjn…D57Uqtmg AJz987nj…X2bMmzq6

481bcbe0a6672c…b4ed22436737ab

1 in → 2 out8.1845 XPM226 B

ARijjV4A…TpVV5Jq7 AeZLowDF…m4c7KEs3

c419acdac49ac8…7ea757727128cd

1 in → 2 out8.1655 XPM227 B

AWjmq4YQ…ceeffmaN AeUNuWiU…PLkCY8bz

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.

1.001 × 10⁹⁸(99-digit number)

10015196148209309714…09659532210699693429

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

1.001 × 10⁹⁸(99-digit number)

10015196148209309714…09659532210699693429

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.001 × 10⁹⁸(99-digit number)

10015196148209309714…09659532210699693431

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

2.003 × 10⁹⁸(99-digit number)

20030392296418619428…19319064421399386859

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.003 × 10⁹⁸(99-digit number)

20030392296418619428…19319064421399386861

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

4.006 × 10⁹⁸(99-digit number)

40060784592837238856…38638128842798773719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.006 × 10⁹⁸(99-digit number)

40060784592837238856…38638128842798773721

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

8.012 × 10⁹⁸(99-digit number)

80121569185674477712…77276257685597547439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.012 × 10⁹⁸(99-digit number)

80121569185674477712…77276257685597547441

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

1.602 × 10⁹⁹(100-digit number)

16024313837134895542…54552515371195094879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.602 × 10⁹⁹(100-digit number)

16024313837134895542…54552515371195094881

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.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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

Cross-reference on Chainz Explorer