Block #1,378,675

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/21/2015, 1:08:01 PM · Difficulty 10.8100 · 5,429,023 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5d9484b752eb84489151654bdd8f9eadedc42bcf8d58cbd041a36c041ee38cd9

View on Chainz ↗

Height

#1,378,675

Difficulty

10.810020

Transactions

Size

3.97 KB

Version

Bits

0acf5d80

Nonce

960,039,154

Timestamp

12/21/2015, 1:08:01 PM

Confirmations

5,429,023

Mined by

⛏️ P2SHAehr8VfsoFNA1QwPogxnuAEs32vzpvH7xN

Merkle Root

f00cfc26be9cc4579de536a7c05840cb3b90241614d8c2e23c369dcf2b381984

Transactions (2)

Coinbase5dd3ec2d4d610c…63b81a9dfd113e

1 in → 1 out8.5800 XPM109 B

Aehr8Vfs…vzpvH7xN

9d038d72d377e1…9e172d1ec4a49d

1 in → 109 out254.3361 XPM3.77 KB

ARRSye9e…oahf7Y1c ASaC5GuA…jnNXWWis AQppDAHZ…HzsaE5ca AKDVUtQS…L1PUaDTn AK3GHp6e…N1s9GLWP

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.

8.488 × 10⁹³(94-digit number)

84884623206389361368…41584110720052591819

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

8.488 × 10⁹³(94-digit number)

84884623206389361368…41584110720052591819

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.488 × 10⁹³(94-digit number)

84884623206389361368…41584110720052591821

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

1.697 × 10⁹⁴(95-digit number)

16976924641277872273…83168221440105183639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.697 × 10⁹⁴(95-digit number)

16976924641277872273…83168221440105183641

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

3.395 × 10⁹⁴(95-digit number)

33953849282555744547…66336442880210367279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.395 × 10⁹⁴(95-digit number)

33953849282555744547…66336442880210367281

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

6.790 × 10⁹⁴(95-digit number)

67907698565111489094…32672885760420734559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.790 × 10⁹⁴(95-digit number)

67907698565111489094…32672885760420734561

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

1.358 × 10⁹⁵(96-digit number)

13581539713022297818…65345771520841469119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.358 × 10⁹⁵(96-digit number)

13581539713022297818…65345771520841469121

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 #1,378,675

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