Block #267,048

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/20/2013, 10:30:55 PM · Difficulty 9.9599 · 6,528,256 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b6fffee9a33af79a5ff56d06c88647249bbd10ce972a6971f20ae0525f13691c

View on Chainz ↗

Height

#267,048

Difficulty

9.959923

Transactions

Size

1.08 KB

Version

Bits

09f5bd85

Nonce

114,166

Timestamp

11/20/2013, 10:30:55 PM

Confirmations

6,528,256

Mined by

⛏️ P2SHANWrHiAp1jAKM5aGHVgFxnabiNY2WAv4pT

Merkle Root

ff2a79418b6dd946ed96b40a5be01249ef86d67e1c824fc81689b800c5fd1908

Transactions (5)

Coinbasec0513000e8e5c7…f82ce9b5d72a83

1 in → 1 out10.1100 XPM109 B

ANWrHiAp…Y2WAv4pT

e380db8d234eb6…8166fd8939ac0e

1 in → 2 out7.1244 XPM226 B

AZdEamjC…nJX3do1F AWcs7SXe…dfop2iY1

5568f5f6f4da0b…ea1f471f1c4bbb

1 in → 2 out4.7315 XPM225 B

AFtyWF4M…39zQkw14 ANh19fKX…c9iagAvJ

fe50d2d303be6b…8415f63203f9a9

1 in → 2 out7.0758 XPM226 B

AL4zxFMe…PmxhRU94 AUtg7hGQ…XFGCgqY7

840ca3b6ba4eb5…a3b500da35ec40

1 in → 2 out6.8940 XPM226 B

APHoVp7u…34nPdQRv AdLJ3UYW…AJC8Yshz

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.

7.747 × 10⁹²(93-digit number)

77470489221136327692…49548954034234330879

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

7.747 × 10⁹²(93-digit number)

77470489221136327692…49548954034234330879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.747 × 10⁹²(93-digit number)

77470489221136327692…49548954034234330881

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

1.549 × 10⁹³(94-digit number)

15494097844227265538…99097908068468661759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.549 × 10⁹³(94-digit number)

15494097844227265538…99097908068468661761

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

3.098 × 10⁹³(94-digit number)

30988195688454531077…98195816136937323519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.098 × 10⁹³(94-digit number)

30988195688454531077…98195816136937323521

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

6.197 × 10⁹³(94-digit number)

61976391376909062154…96391632273874647039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.197 × 10⁹³(94-digit number)

61976391376909062154…96391632273874647041

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

1.239 × 10⁹⁴(95-digit number)

12395278275381812430…92783264547749294079

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