Block #1,080,687

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/29/2015, 2:20:20 AM · Difficulty 10.7641 · 5,726,920 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

25794e3cae17d51e7d8c5b52d7a52453e81271eaa4bc9eb184285b2d5860bc21

View on Chainz ↗

Height

#1,080,687

Difficulty

10.764079

Transactions

Size

1.01 KB

Version

Bits

0ac39ab6

Nonce

1,406,102,787

Timestamp

5/29/2015, 2:20:20 AM

Confirmations

5,726,920

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0235548af8244d4046dee36406dd640b55ee1814026987932a90f11982684aa6

Transactions (4)

Coinbasec3576350880174…f3006dd40c8069

1 in → 1 out8.6500 XPM116 B

ANSXnLY2…Sd25TjkD

332c50efb180b0…f667639f2f0cd0

2 in → 2 out16.2662 XPM374 B

ANNBoEaA…o6TzGWqw AaKw6snj…YNADhA1s

4d6150457ec443…4002777e8e62c1

1 in → 2 out8.6200 XPM226 B

AVZwze3C…1DNKwKx6 AGo3Kb7A…CH1dLLs9

b685b37405ebe3…0a78bf7c239b74

1 in → 2 out8.6200 XPM225 B

AMqvbAMs…Ra8XriVo AHmcchxr…vBbydp5n

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.

3.830 × 10⁹⁸(99-digit number)

38309585877755439222…11718850386303836159

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

3.830 × 10⁹⁸(99-digit number)

38309585877755439222…11718850386303836159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.830 × 10⁹⁸(99-digit number)

38309585877755439222…11718850386303836161

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

7.661 × 10⁹⁸(99-digit number)

76619171755510878444…23437700772607672319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.661 × 10⁹⁸(99-digit number)

76619171755510878444…23437700772607672321

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

1.532 × 10⁹⁹(100-digit number)

15323834351102175688…46875401545215344639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.532 × 10⁹⁹(100-digit number)

15323834351102175688…46875401545215344641

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

3.064 × 10⁹⁹(100-digit number)

30647668702204351377…93750803090430689279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.064 × 10⁹⁹(100-digit number)

30647668702204351377…93750803090430689281

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

6.129 × 10⁹⁹(100-digit number)

61295337404408702755…87501606180861378559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.129 × 10⁹⁹(100-digit number)

61295337404408702755…87501606180861378561

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 #1,080,687

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