Block #1,394,290

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/1/2016, 8:18:08 AM · Difficulty 10.8130 · 5,432,146 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8191bce79056aaf222e1d26b3c606c46cecf264927661331d08bbfaef9ca628b

View on Chainz ↗

Height

#1,394,290

Difficulty

10.812990

Transactions

Size

2.44 KB

Version

Bits

0ad0201c

Nonce

1,470,263,647

Timestamp

1/1/2016, 8:18:08 AM

Confirmations

5,432,146

Mined by

⛏️ P2SHAQd4GkRsfRQ1YXTohqvXB6S4XdVVR1MB5g

Merkle Root

7fae96972d1082b8b54d040edd53532f098d240ff65dac17ac2e5409c1b827c5

Transactions (2)

Coinbase50b2776b01f6f5…57058a0c6ae66e

1 in → 1 out8.5700 XPM110 B

AQd4GkRs…VVR1MB5g

99636ce7095833…dad94b20f832ca

15 in → 2 out1.3058 XPM2.24 KB

ASeoFGwY…REXLsSxz AVZMg6c5…cCvX8ivi

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.

5.152 × 10⁹⁸(99-digit number)

51521561285764503517…18048761939969802239

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

5.152 × 10⁹⁸(99-digit number)

51521561285764503517…18048761939969802239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.152 × 10⁹⁸(99-digit number)

51521561285764503517…18048761939969802241

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

1.030 × 10⁹⁹(100-digit number)

10304312257152900703…36097523879939604479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.030 × 10⁹⁹(100-digit number)

10304312257152900703…36097523879939604481

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

2.060 × 10⁹⁹(100-digit number)

20608624514305801407…72195047759879208959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.060 × 10⁹⁹(100-digit number)

20608624514305801407…72195047759879208961

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

4.121 × 10⁹⁹(100-digit number)

41217249028611602814…44390095519758417919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.121 × 10⁹⁹(100-digit number)

41217249028611602814…44390095519758417921

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

8.243 × 10⁹⁹(100-digit number)

82434498057223205628…88780191039516835839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.243 × 10⁹⁹(100-digit number)

82434498057223205628…88780191039516835841

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 #1,394,290

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