Block #1,105,186

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/14/2015, 9:26:45 PM · Difficulty 10.7791 · 5,709,048 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

63256b860dedb3167dad0ea4485a66106454623e47d7df84a28965e13178e9b8

View on Chainz ↗

Height

#1,105,186

Difficulty

10.779050

Transactions

Size

2.05 KB

Version

Bits

0ac76fd3

Nonce

308,251,936

Timestamp

6/14/2015, 9:26:45 PM

Confirmations

5,709,048

Mined by

⛏️ P2SHAThHew5Hj5righL4PRaYTpHH3TGY1krHtL

Merkle Root

e6efc44b17804c658bcb2fd955861d28f704e4b2564ed3d82f2df6a48ac5a2d7

Transactions (3)

Coinbase95b4ea9972a3f0…b72c71071677f7

1 in → 1 out8.6200 XPM109 B

AThHew5H…GY1krHtL

ab6a4da9ba3b6c…e7be50c1302918

9 in → 1 out199.9900 XPM1.34 KB

ARCu8oQG…9DP3FpT6

1128cdfcce38ef…07ef74de51b338

3 in → 2 out12.6014 XPM522 B

AShjFofc…oEVPwhaE AK9LxQQh…h24pctRm

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.

8.596 × 10⁹⁵(96-digit number)

85964154164517262904…06175058005206329919

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

8.596 × 10⁹⁵(96-digit number)

85964154164517262904…06175058005206329919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.596 × 10⁹⁵(96-digit number)

85964154164517262904…06175058005206329921

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

1.719 × 10⁹⁶(97-digit number)

17192830832903452580…12350116010412659839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.719 × 10⁹⁶(97-digit number)

17192830832903452580…12350116010412659841

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

3.438 × 10⁹⁶(97-digit number)

34385661665806905161…24700232020825319679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.438 × 10⁹⁶(97-digit number)

34385661665806905161…24700232020825319681

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

6.877 × 10⁹⁶(97-digit number)

68771323331613810323…49400464041650639359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.877 × 10⁹⁶(97-digit number)

68771323331613810323…49400464041650639361

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

1.375 × 10⁹⁷(98-digit number)

13754264666322762064…98800928083301278719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.375 × 10⁹⁷(98-digit number)

13754264666322762064…98800928083301278721

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 #1,105,186

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