Block #2,784,886

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 8/8/2018, 1:13:02 PM · Difficulty 11.6689 · 4,041,225 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d9d86b2992e30c0e9c6db74e6282968b5ae07740a2127e7728750892b25b0a67

View on Chainz ↗

Height

#2,784,886

Difficulty

11.668901

Transactions

Size

1.36 KB

Version

Bits

0bab3d19

Nonce

448,439,374

Timestamp

8/8/2018, 1:13:02 PM

Confirmations

4,041,225

Mined by

⛏️ P2SHASvHkepRCxoCSeCYwsCGrc1DNGusJ1rWpt

Merkle Root

631a1ded06564a8710b80bcc01d143b9485e67def3557da15c49251a8fdc0165

Transactions (3)

Coinbase81cd3b302c2d34…4a8643ed1ab9d9

1 in → 1 out7.3500 XPM110 B

ASvHkepR…usJ1rWpt

a0c413a7faf892…d6353c4ff2c093

5 in → 2 out3.6628 XPM817 B

APi8C85f…Lg5MDiei AYVd1Rtm…gizeh8jo

ad39da28086a42…711a46db63b2e6

2 in → 2 out7.6428 XPM374 B

AZ4UnHzJ…PH7NQioA AKgrbWPM…dkwB2FD9

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.

1.368 × 10⁹⁷(98-digit number)

13685979491858416732…40074628924228177919

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

1.368 × 10⁹⁷(98-digit number)

13685979491858416732…40074628924228177919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.368 × 10⁹⁷(98-digit number)

13685979491858416732…40074628924228177921

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

2.737 × 10⁹⁷(98-digit number)

27371958983716833465…80149257848456355839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.737 × 10⁹⁷(98-digit number)

27371958983716833465…80149257848456355841

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

5.474 × 10⁹⁷(98-digit number)

54743917967433666930…60298515696912711679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.474 × 10⁹⁷(98-digit number)

54743917967433666930…60298515696912711681

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

1.094 × 10⁹⁸(99-digit number)

10948783593486733386…20597031393825423359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.094 × 10⁹⁸(99-digit number)

10948783593486733386…20597031393825423361

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

2.189 × 10⁹⁸(99-digit number)

21897567186973466772…41194062787650846719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.189 × 10⁹⁸(99-digit number)

21897567186973466772…41194062787650846721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.379 × 10⁹⁸(99-digit number)

43795134373946933544…82388125575301693439

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

4.379 × 10⁹⁸(99-digit number)

43795134373946933544…82388125575301693441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,784,886

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