Block #271,291

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 1:06:35 PM · Difficulty 9.9517 · 6,518,792 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a1ad92f059829fb6b111e8d89afb8f57e46316dc783bcccf83e8f13465b0c4c

View on Chainz ↗

Height

#271,291

Difficulty

9.951741

Transactions

Size

199 B

Version

Bits

09f3a553

Nonce

61,253

Timestamp

11/24/2013, 1:06:35 PM

Confirmations

6,518,792

Merkle Root

e275027960fd0136c432e2f5559e42688089b17e557e7a4c1a9d8003a06514a5

Transactions (1)

Coinbasee275027960fd01…9d8003a06514a5

1 in → 1 out10.0800 XPM109 B

AWT4FajA…7qUxCsaJ

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.

4.997 × 10⁹⁵(96-digit number)

49975866819180970329…08347503273108456879

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

4.997 × 10⁹⁵(96-digit number)

49975866819180970329…08347503273108456879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.997 × 10⁹⁵(96-digit number)

49975866819180970329…08347503273108456881

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

9.995 × 10⁹⁵(96-digit number)

99951733638361940659…16695006546216913759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.995 × 10⁹⁵(96-digit number)

99951733638361940659…16695006546216913761

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

1.999 × 10⁹⁶(97-digit number)

19990346727672388131…33390013092433827519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.999 × 10⁹⁶(97-digit number)

19990346727672388131…33390013092433827521

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

3.998 × 10⁹⁶(97-digit number)

39980693455344776263…66780026184867655039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.998 × 10⁹⁶(97-digit number)

39980693455344776263…66780026184867655041

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

7.996 × 10⁹⁶(97-digit number)

79961386910689552527…33560052369735310079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.996 × 10⁹⁶(97-digit number)

79961386910689552527…33560052369735310081

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