Block #290,307

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 3:16:20 PM · Difficulty 9.9891 · 6,525,749 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c496c89986500e485c0161dc561a7969fe1fb7c1527407479c4b7a74f6f59188

View on Chainz ↗

Height

#290,307

Difficulty

9.989133

Transactions

Size

935 B

Version

Bits

09fd37ce

Nonce

69,415

Timestamp

12/2/2013, 3:16:20 PM

Confirmations

6,525,749

Mined by

⛏️ naR4^AZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

0103fee3221d68d557157ece5efcf1b00db3ebc8e4ab7a0844be0bf581f33b79

Transactions (1)

Coinbase0103fee3221d68…be0bf581f33b79

1 in → 23 out10.0100 XPM845 B

AZninDSu…FvgDMwC4 Ae58nAEb…GFUA15fv AWm233nS…1dJSnVJJ Ad9pSzHt…cpJ3y2zz AZ2pPuKg…95SN2Yr7

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.

9.458 × 10⁹⁴(95-digit number)

94587879616991872343…62672390761375226529

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

9.458 × 10⁹⁴(95-digit number)

94587879616991872343…62672390761375226529

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.458 × 10⁹⁴(95-digit number)

94587879616991872343…62672390761375226531

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

1.891 × 10⁹⁵(96-digit number)

18917575923398374468…25344781522750453059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.891 × 10⁹⁵(96-digit number)

18917575923398374468…25344781522750453061

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

3.783 × 10⁹⁵(96-digit number)

37835151846796748937…50689563045500906119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.783 × 10⁹⁵(96-digit number)

37835151846796748937…50689563045500906121

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

7.567 × 10⁹⁵(96-digit number)

75670303693593497874…01379126091001812239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.567 × 10⁹⁵(96-digit number)

75670303693593497874…01379126091001812241

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

1.513 × 10⁹⁶(97-digit number)

15134060738718699574…02758252182003624479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.513 × 10⁹⁶(97-digit number)

15134060738718699574…02758252182003624481

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

Block #290,307

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