Block #186,192

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 6:42:30 PM · Difficulty 9.8646 · 6,605,245 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

db44bfe4769833029b8310ed88298d2899ede9a0457e90cd9f08e2fe2086e6e0

View on Chainz ↗

Height

#186,192

Difficulty

9.864578

Transactions

Size

203 B

Version

Bits

09dd54fc

Nonce

117,441,198

Timestamp

9/29/2013, 6:42:30 PM

Confirmations

6,605,245

Merkle Root

a48c3eaecea7db5409c1453030d508b693a114000355b465cf91e8a31e0cd386

Transactions (1)

Coinbasea48c3eaecea7db…91e8a31e0cd386

1 in → 1 out10.2600 XPM116 B

AcLBm5Z9…S683d7c3

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.

1.126 × 10⁸⁸(89-digit number)

11262241035348585422…78772712250359163519

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

1.126 × 10⁸⁸(89-digit number)

11262241035348585422…78772712250359163519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.126 × 10⁸⁸(89-digit number)

11262241035348585422…78772712250359163521

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

2.252 × 10⁸⁸(89-digit number)

22524482070697170844…57545424500718327039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.252 × 10⁸⁸(89-digit number)

22524482070697170844…57545424500718327041

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

4.504 × 10⁸⁸(89-digit number)

45048964141394341688…15090849001436654079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.504 × 10⁸⁸(89-digit number)

45048964141394341688…15090849001436654081

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

9.009 × 10⁸⁸(89-digit number)

90097928282788683376…30181698002873308159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.009 × 10⁸⁸(89-digit number)

90097928282788683376…30181698002873308161

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

1.801 × 10⁸⁹(90-digit number)

18019585656557736675…60363396005746616319

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