Block #295,491

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/5/2013, 11:37:29 AM · Difficulty 9.9914 · 6,497,562 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa9bc2bfbb723fcc10af0afd95b7099f46a65c444e0d38a16a4fbd864ac05b9d

View on Chainz ↗

Height

#295,491

Difficulty

9.991391

Transactions

Size

1.55 KB

Version

Bits

09fdcbc7

Nonce

123,229

Timestamp

12/5/2013, 11:37:29 AM

Confirmations

6,497,562

Merkle Root

63b2302f0502b2e1dc1c7a8df1a2bca18f5a67836009ac29c3db7c6c83ab625e

Transactions (2)

Coinbase2535e92b0713a1…d59fb13e2f3ee5

1 in → 24 out10.0000 XPM879 B

AcGg26YC…5FqokLdr AWuQdP8q…6YMDw92f ARZooKAK…ud8Bftqw AKEwr54i…9BfmMkRh ATSUeWML…N6kUrgvS

d9b9f68d7ca12f…abfe5845236f2e

3 in → 5 out1568.8056 XPM623 B

AQqtVpbi…TK2PyKrX AdoL4h3K…5iB8iY1U AMS434LY…ySngY6w4 AJhpAoLd…wcEQZVmm ATDg1wpK…dc5kwZ3e

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.

4.537 × 10⁹⁰(91-digit number)

45375623305675763705…09020740015108486439

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

4.537 × 10⁹⁰(91-digit number)

45375623305675763705…09020740015108486439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.537 × 10⁹⁰(91-digit number)

45375623305675763705…09020740015108486441

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

9.075 × 10⁹⁰(91-digit number)

90751246611351527410…18041480030216972879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.075 × 10⁹⁰(91-digit number)

90751246611351527410…18041480030216972881

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

1.815 × 10⁹¹(92-digit number)

18150249322270305482…36082960060433945759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.815 × 10⁹¹(92-digit number)

18150249322270305482…36082960060433945761

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

3.630 × 10⁹¹(92-digit number)

36300498644540610964…72165920120867891519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.630 × 10⁹¹(92-digit number)

36300498644540610964…72165920120867891521

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

7.260 × 10⁹¹(92-digit number)

72600997289081221928…44331840241735783039

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