Block #251,791

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 5:34:45 AM · Difficulty 9.9703 · 6,544,947 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6c55aa50c79b7887495ce04bc22bf7aa34347c374b90c94c630f02b63a495780

View on Chainz ↗

Height

#251,791

Difficulty

9.970291

Transactions

Size

1.65 KB

Version

Bits

09f864f7

Nonce

219,953

Timestamp

11/9/2013, 5:34:45 AM

Confirmations

6,544,947

Mined by

⛏️ P2SHAPkdeq7s4dFoPuKgy9yUh9eB611LH3o2XK

Merkle Root

770ed2357b3ff04e20a3186d1c5bbdc8f86a611a3688ab9c2c50205dd23e20d9

Transactions (3)

Coinbasec552a72da8d77c…c0006ce1dc9dc8

1 in → 1 out10.0600 XPM109 B

APkdeq7s…1LH3o2XK

8ea72cf377b30a…3823e4c99bb0e9

3 in → 2 out2.9847 XPM521 B

AcRZ1X4a…WRJA3LEE ATDfGxni…F5K4kNtN

b0495aa7c540c8…414ce7c2fbbb90

6 in → 2 out3.3525 XPM969 B

AK6itGuo…u5HWghLK AcRZ1X4a…WRJA3LEE

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.

8.401 × 10⁹³(94-digit number)

84015126346880802662…44626665068021448239

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

8.401 × 10⁹³(94-digit number)

84015126346880802662…44626665068021448239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.401 × 10⁹³(94-digit number)

84015126346880802662…44626665068021448241

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

1.680 × 10⁹⁴(95-digit number)

16803025269376160532…89253330136042896479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.680 × 10⁹⁴(95-digit number)

16803025269376160532…89253330136042896481

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

3.360 × 10⁹⁴(95-digit number)

33606050538752321064…78506660272085792959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.360 × 10⁹⁴(95-digit number)

33606050538752321064…78506660272085792961

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

6.721 × 10⁹⁴(95-digit number)

67212101077504642129…57013320544171585919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.721 × 10⁹⁴(95-digit number)

67212101077504642129…57013320544171585921

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

1.344 × 10⁹⁵(96-digit number)

13442420215500928425…14026641088343171839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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