Block #435,783

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/9/2014, 4:21:22 AM · Difficulty 10.3533 · 6,369,257 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

550b408ee0f716e37b5b2f98fc0474b46f620e48defa75847b1bb809bbdfafb8

View on Chainz ↗

Height

#435,783

Difficulty

10.353280

Transactions

Size

968 B

Version

Bits

0a5a7088

Nonce

6,977

Timestamp

3/9/2014, 4:21:22 AM

Confirmations

6,369,257

Mined by

⛏️ GaS7=AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d20b25d70c3781dce1c51593a46cb61859f67426467b375b09041a6ea956af49

Transactions (1)

Coinbased20b25d70c3781…041a6ea956af49

1 in → 24 out9.3100 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGD4yZQw…hGzM2XAx ATKK7iFz…wZm46KN1 AScAzqGc…BZ6tV1vJ

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.

1.318 × 10⁹³(94-digit number)

13184682197693095926…29421302426744688639

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

1.318 × 10⁹³(94-digit number)

13184682197693095926…29421302426744688639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.318 × 10⁹³(94-digit number)

13184682197693095926…29421302426744688641

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

2.636 × 10⁹³(94-digit number)

26369364395386191853…58842604853489377279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.636 × 10⁹³(94-digit number)

26369364395386191853…58842604853489377281

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

5.273 × 10⁹³(94-digit number)

52738728790772383707…17685209706978754559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.273 × 10⁹³(94-digit number)

52738728790772383707…17685209706978754561

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

1.054 × 10⁹⁴(95-digit number)

10547745758154476741…35370419413957509119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.054 × 10⁹⁴(95-digit number)

10547745758154476741…35370419413957509121

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

2.109 × 10⁹⁴(95-digit number)

21095491516308953482…70740838827915018239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.109 × 10⁹⁴(95-digit number)

21095491516308953482…70740838827915018241

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