Block #1,185,028

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/6/2015, 9:55:45 PM · Difficulty 10.8934 · 5,657,481 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

31939bdb87939d630e7dfb805c560a093b7ec33e54648c9430a9835a0662d950

View on Chainz ↗

Height

#1,185,028

Difficulty

10.893442

Transactions

Size

3.74 KB

Version

Bits

0ae4b897

Nonce

1,274,843,159

Timestamp

8/6/2015, 9:55:45 PM

Confirmations

5,657,481

Mined by

⛏️ P2SHAQGWfsRoTkJhrTrM5HUXj1ksemee8ovk2U

Merkle Root

186df445f0d86bd99f4e54bf208e34233803eb0122971ecc05d88db4978227b7

Transactions (2)

Coinbase9560da1e7738ef…1bce8ad1ae7ada

1 in → 1 out8.4500 XPM109 B

AQGWfsRo…ee8ovk2U

1b2d4580f2f9c0…b4cf941e401ad8

24 in → 2 out6622.8948 XPM3.54 KB

AFpjh6Bk…tYhNEcvN AdzeZd8K…BGECBKQC

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.

1.900 × 10⁹²(93-digit number)

19001503174958796709…37826204867030909599

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

1.900 × 10⁹²(93-digit number)

19001503174958796709…37826204867030909599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.900 × 10⁹²(93-digit number)

19001503174958796709…37826204867030909601

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

3.800 × 10⁹²(93-digit number)

38003006349917593419…75652409734061819199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.800 × 10⁹²(93-digit number)

38003006349917593419…75652409734061819201

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

7.600 × 10⁹²(93-digit number)

76006012699835186838…51304819468123638399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.600 × 10⁹²(93-digit number)

76006012699835186838…51304819468123638401

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

1.520 × 10⁹³(94-digit number)

15201202539967037367…02609638936247276799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.520 × 10⁹³(94-digit number)

15201202539967037367…02609638936247276801

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

3.040 × 10⁹³(94-digit number)

30402405079934074735…05219277872494553599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.040 × 10⁹³(94-digit number)

30402405079934074735…05219277872494553601

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 #1,185,028

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