Block #1,106,946

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/15/2015, 1:41:32 PM · Difficulty 10.8110 · 5,702,744 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

840f3faba7fd3914d9e530dbad4a12ebf5eac39b83a820330822ba01d779590a

View on Chainz ↗

Height

#1,106,946

Difficulty

10.810969

Transactions

Size

46.29 KB

Version

Bits

0acf9bac

Nonce

1,303,324,150

Timestamp

6/15/2015, 1:41:32 PM

Confirmations

5,702,744

Mined by

⛏️ P2SHANjbvPKPjdtvBhV56kWCGvTCEHzwFyzn8z

Merkle Root

8e1b87d2a2cbe7d7d58ddec6160625af5bc45f4ab49a4ec3d4b97910c32f6dce

Transactions (3)

Coinbase6656d658a8d637…a7e74026b805bc

1 in → 1 out9.1200 XPM110 B

ANjbvPKP…zwFyzn8z

9473ee79361af6…ed14452f1c4b59

317 in → 2 out520.9429 XPM45.87 KB

AQHE5e6H…xDwU3vYU APimRhFp…1Vz7wNKv

7e2ef77ced2895…ea4b25e72d8fee

1 in → 2 out2.0065 XPM226 B

AP1Qrs3B…3KhMfvnA AUws6rQ3…Q7q8MhbV

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.

1.989 × 10⁹⁷(98-digit number)

19898501316845008825…93450422841477201919

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

1.989 × 10⁹⁷(98-digit number)

19898501316845008825…93450422841477201919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.989 × 10⁹⁷(98-digit number)

19898501316845008825…93450422841477201921

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

3.979 × 10⁹⁷(98-digit number)

39797002633690017650…86900845682954403839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.979 × 10⁹⁷(98-digit number)

39797002633690017650…86900845682954403841

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

7.959 × 10⁹⁷(98-digit number)

79594005267380035301…73801691365908807679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.959 × 10⁹⁷(98-digit number)

79594005267380035301…73801691365908807681

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

1.591 × 10⁹⁸(99-digit number)

15918801053476007060…47603382731817615359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.591 × 10⁹⁸(99-digit number)

15918801053476007060…47603382731817615361

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

3.183 × 10⁹⁸(99-digit number)

31837602106952014120…95206765463635230719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.183 × 10⁹⁸(99-digit number)

31837602106952014120…95206765463635230721

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 #1,106,946

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