Block #275,146

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 2:08:34 PM · Difficulty 9.9599 · 6,520,756 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d31197ea342c9bdf2cfffbc8e49bcd6555337940a3900705b662141dc15a348

View on Chainz ↗

Height

#275,146

Difficulty

9.959881

Transactions

Size

460 B

Version

Bits

09f5bac4

Nonce

32,960

Timestamp

11/26/2013, 2:08:34 PM

Confirmations

6,520,756

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

53f60f10f84779cd37025168fd5b0de0fff413d674f6edb14410b79b3fb688f6

Transactions (2)

Coinbase4e7555c5657f5a…ec76e36a0bccd4

1 in → 2 out10.0800 XPM140 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

80f06f7429ed9d…d0dc086ce7696f

1 in → 2 out75.0895 XPM226 B

AJi4HR4A…2QX5Ag1T AYmzdtJB…hiasyn2t

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.

3.099 × 10¹⁰⁴(105-digit number)

30999681639135522997…85886868507266755199

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

3.099 × 10¹⁰⁴(105-digit number)

30999681639135522997…85886868507266755199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.099 × 10¹⁰⁴(105-digit number)

30999681639135522997…85886868507266755201

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

6.199 × 10¹⁰⁴(105-digit number)

61999363278271045995…71773737014533510399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.199 × 10¹⁰⁴(105-digit number)

61999363278271045995…71773737014533510401

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

1.239 × 10¹⁰⁵(106-digit number)

12399872655654209199…43547474029067020799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.239 × 10¹⁰⁵(106-digit number)

12399872655654209199…43547474029067020801

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

2.479 × 10¹⁰⁵(106-digit number)

24799745311308418398…87094948058134041599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.479 × 10¹⁰⁵(106-digit number)

24799745311308418398…87094948058134041601

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

4.959 × 10¹⁰⁵(106-digit number)

49599490622616836796…74189896116268083199

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