Block #276,317

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 3:17:37 AM · Difficulty 9.9628 · 6,529,371 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6b1d403144fae3c24fa42901c8cf09c1d07b0a9a638a86c30684595e77507551

View on Chainz ↗

Height

#276,317

Difficulty

9.962845

Transactions

Size

1.14 KB

Version

Bits

09f67d03

Nonce

209,897

Timestamp

11/27/2013, 3:17:37 AM

Confirmations

6,529,371

Mined by

⛏️ 7aRdZAVss9H5FkXhhqqTXyhqhrXDK3UzXhyMijY

Merkle Root

a938afc591202ede01a941fa747cc902b56f8bec537e7194c96620d52ff593d3

Transactions (1)

Coinbasea938afc591202e…6620d52ff593d3

1 in → 30 out10.0400 XPM1.06 KB

AVss9H5F…zXhyMijY ANeVYf1h…zLosYoJL AY9F7Byy…EfAVw9Yf Acs9SHrk…QJSB8SFG AcP9aGkN…9c7TeeiQ

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.

1.429 × 10⁹²(93-digit number)

14290273131054947193…65701030586488707759

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

1.429 × 10⁹²(93-digit number)

14290273131054947193…65701030586488707759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.429 × 10⁹²(93-digit number)

14290273131054947193…65701030586488707761

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

2.858 × 10⁹²(93-digit number)

28580546262109894387…31402061172977415519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.858 × 10⁹²(93-digit number)

28580546262109894387…31402061172977415521

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

5.716 × 10⁹²(93-digit number)

57161092524219788775…62804122345954831039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.716 × 10⁹²(93-digit number)

57161092524219788775…62804122345954831041

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

1.143 × 10⁹³(94-digit number)

11432218504843957755…25608244691909662079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.143 × 10⁹³(94-digit number)

11432218504843957755…25608244691909662081

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

2.286 × 10⁹³(94-digit number)

22864437009687915510…51216489383819324159

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