Block #184,773

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/28/2013, 9:07:28 PM · Difficulty 9.8609 · 6,618,631 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

87b6c66b9a59e527c962b9df5dc7e3f6f47e438a9cdcefbd9203b5496d4d8b28

View on Chainz ↗

Height

#184,773

Difficulty

9.860907

Transactions

Size

575 B

Version

Bits

09dc6466

Nonce

127

Timestamp

9/28/2013, 9:07:28 PM

Confirmations

6,618,631

Mined by

⛏️ P2SHANvtpRa12yh2D3uGdgT2ggcH58QjsraDJz

Merkle Root

334dcdd92a9705ae109d7e22486a329a47ee317f31ea1d4aeac82a6180eeb984

Transactions (2)

Coinbase12b65843d8181d…d51b359f24e20e

1 in → 1 out10.2800 XPM110 B

ANvtpRa1…QjsraDJz

f23be9ca57834d…55c346fefb1d24

2 in → 2 out200.9800 XPM374 B

Aaf6GQiz…ACjux9Zg Ab6XQdqw…TCF9niBG

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.

8.309 × 10⁹⁷(98-digit number)

83091004657096757213…36660723935865951999

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

8.309 × 10⁹⁷(98-digit number)

83091004657096757213…36660723935865951999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.309 × 10⁹⁷(98-digit number)

83091004657096757213…36660723935865952001

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

1.661 × 10⁹⁸(99-digit number)

16618200931419351442…73321447871731903999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.661 × 10⁹⁸(99-digit number)

16618200931419351442…73321447871731904001

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

3.323 × 10⁹⁸(99-digit number)

33236401862838702885…46642895743463807999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.323 × 10⁹⁸(99-digit number)

33236401862838702885…46642895743463808001

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

6.647 × 10⁹⁸(99-digit number)

66472803725677405770…93285791486927615999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.647 × 10⁹⁸(99-digit number)

66472803725677405770…93285791486927616001

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

1.329 × 10⁹⁹(100-digit number)

13294560745135481154…86571582973855231999

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