Block #365,162

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2014, 1:42:32 PM · Difficulty 10.4235 · 6,451,928 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c8f1b01a0b526f83ca73e5f4b6c3a4835f986fff7592d1f86c3548478f76fb46

View on Chainz ↗

Height

#365,162

Difficulty

10.423466

Transactions

Size

1.50 KB

Version

Bits

0a6c6844

Nonce

86,861

Timestamp

1/18/2014, 1:42:32 PM

Confirmations

6,451,928

Mined by

⛏️ j0Ac2JYASPQD7vWBs42nkRqpCmFvtcBL5PEW

Merkle Root

19bd205d3aa4550f36286eaf7117bcf215e206033f3815a130eea3b4df351bf5

Transactions (5)

Coinbase03c10c6157027d…02db2d0260a019

1 in → 2 out9.2300 XPM131 B

Ac2JYASP…tcBL5PEW AJno7LX2…vo4wdWtY

7f2727611f7eb0…03a4885198f3ac

1 in → 2 out9.2000 XPM226 B

AcSazGwM…J7PyVZKR AbkDEHdb…6E5nCuim

a90b9f09de8d6f…7d6d5835765f6a

4 in → 2 out4.5247 XPM671 B

APLxNhiM…9V6xzb7Y AM2Puo9h…M6knVc8L

ac918f096f9d4f…ee39ce35afbee1

1 in → 1 out2.9945 XPM191 B

APiiSQDW…QoCPjFQC

6ea5b4a85ab9c6…949c5e2a47c098

1 in → 2 out8.1932 XPM226 B

ALmGrQGD…C63tZAot AZwyMUeE…rxMQeLU7

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.

3.092 × 10⁹⁷(98-digit number)

30922390005934762813…60887293635860582399

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

3.092 × 10⁹⁷(98-digit number)

30922390005934762813…60887293635860582399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.092 × 10⁹⁷(98-digit number)

30922390005934762813…60887293635860582401

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

6.184 × 10⁹⁷(98-digit number)

61844780011869525627…21774587271721164799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.184 × 10⁹⁷(98-digit number)

61844780011869525627…21774587271721164801

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

1.236 × 10⁹⁸(99-digit number)

12368956002373905125…43549174543442329599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.236 × 10⁹⁸(99-digit number)

12368956002373905125…43549174543442329601

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

2.473 × 10⁹⁸(99-digit number)

24737912004747810251…87098349086884659199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.473 × 10⁹⁸(99-digit number)

24737912004747810251…87098349086884659201

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

4.947 × 10⁹⁸(99-digit number)

49475824009495620502…74196698173769318399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.947 × 10⁹⁸(99-digit number)

49475824009495620502…74196698173769318401

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

Block #365,162

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