Block #1,252,779

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/25/2015, 10:36:44 AM · Difficulty 10.7860 · 5,574,357 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

73fc64ed3ee3ac50dc59973656382af7f4bc5cdcdf4310a692c2a827b3dbb0a6

View on Chainz ↗

Height

#1,252,779

Difficulty

10.785978

Transactions

Size

11.88 KB

Version

Bits

0ac935d5

Nonce

1,335,540,370

Timestamp

9/25/2015, 10:36:44 AM

Confirmations

5,574,357

Mined by

⛏️ P2SHAT7dPWWUoNdsfQVWgDJP9TSZjRkbtME7HC

Merkle Root

1063f67a6d31ede06e348fbb1836813db64bb4638bf49ce2d1018654c1a19c75

Transactions (3)

Coinbased2125fb9ac7267…b6a9e8cd92d512

1 in → 1 out8.7100 XPM109 B

AT7dPWWU…kbtME7HC

ab88ad0e65668c…77de04bb321659

1 in → 2 out8.6000 XPM226 B

AMHwFQ7F…S6fNESwY AGwoeKkd…qvXJB4mz

51bd5f93520cc4…2721462a9944d0

79 in → 1 out6.2897 XPM11.47 KB

ASv8QCCi…HPGBuiyg

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.

5.314 × 10⁹⁴(95-digit number)

53144213469073871898…60329065014218298199

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

5.314 × 10⁹⁴(95-digit number)

53144213469073871898…60329065014218298199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.314 × 10⁹⁴(95-digit number)

53144213469073871898…60329065014218298201

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

1.062 × 10⁹⁵(96-digit number)

10628842693814774379…20658130028436596399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.062 × 10⁹⁵(96-digit number)

10628842693814774379…20658130028436596401

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

2.125 × 10⁹⁵(96-digit number)

21257685387629548759…41316260056873192799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.125 × 10⁹⁵(96-digit number)

21257685387629548759…41316260056873192801

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

4.251 × 10⁹⁵(96-digit number)

42515370775259097519…82632520113746385599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.251 × 10⁹⁵(96-digit number)

42515370775259097519…82632520113746385601

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

8.503 × 10⁹⁵(96-digit number)

85030741550518195038…65265040227492771199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.503 × 10⁹⁵(96-digit number)

85030741550518195038…65265040227492771201

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 #1,252,779

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