Block #269,092

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 6:07:25 PM · Difficulty 9.9552 · 6,522,872 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

458f865328edee30fe27fd284ec808288d75dbb5c0d781e22f90db864a5b5083

View on Chainz ↗

Height

#269,092

Difficulty

9.955185

Transactions

Size

424 B

Version

Bits

09f48707

Nonce

29,834

Timestamp

11/22/2013, 6:07:25 PM

Confirmations

6,522,872

Merkle Root

4985b9b0ee2dc37ca1d74ca1e704630b2114a7165ae294dcb222291be2b20b8b

Transactions (2)

Coinbasefa61454ec7b2fe…7f817bc1951008

1 in → 1 out10.0900 XPM109 B

AVnnukKe…9qQ312cc

9281f0b12cbc2e…91787c88c9f569

1 in → 2 out5.0126 XPM225 B

AN1TFSv4…iKjVAUE3 AbTf5Xac…yygV7f7c

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.

8.078 × 10⁹³(94-digit number)

80785622259392998624…04714917476476104519

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

8.078 × 10⁹³(94-digit number)

80785622259392998624…04714917476476104519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.078 × 10⁹³(94-digit number)

80785622259392998624…04714917476476104521

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

1.615 × 10⁹⁴(95-digit number)

16157124451878599724…09429834952952209039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.615 × 10⁹⁴(95-digit number)

16157124451878599724…09429834952952209041

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

3.231 × 10⁹⁴(95-digit number)

32314248903757199449…18859669905904418079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.231 × 10⁹⁴(95-digit number)

32314248903757199449…18859669905904418081

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

6.462 × 10⁹⁴(95-digit number)

64628497807514398899…37719339811808836159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.462 × 10⁹⁴(95-digit number)

64628497807514398899…37719339811808836161

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

1.292 × 10⁹⁵(96-digit number)

12925699561502879779…75438679623617672319

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