Block #2,646,332

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 7:43:14 AM · Difficulty 11.7483 · 4,184,296 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d0bdd334a4920dcbebde9cec5e76b0aeeab4a5438a332ade977ff1333e3ad75

View on Chainz ↗

Height

#2,646,332

Difficulty

11.748301

Transactions

Size

426 B

Version

Bits

0bbf90a2

Nonce

816,174,205

Timestamp

5/3/2018, 7:43:14 AM

Confirmations

4,184,296

Mined by

⛏️ P2SHAUhJVwbLmhdCgkLYMLDnXNNRPCjdQ5xCVS

Merkle Root

14a98539cceaa7ddbce71b2a827768b2cda62b41ae5f8083092b5c320437ee31

Transactions (2)

Coinbasee829d803104ee8…2fa954924fd2f4

1 in → 1 out7.2400 XPM110 B

AUhJVwbL…jdQ5xCVS

9328631d6aa4b3…5cbc7b58af2375

1 in → 2 out18.9330 XPM225 B

AUMAFvFG…U3tviQiX AX2JD8cr…YtZp5NKo

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.

5.883 × 10⁹⁷(98-digit number)

58832612208573370091…50106719388286320639

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

5.883 × 10⁹⁷(98-digit number)

58832612208573370091…50106719388286320639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.883 × 10⁹⁷(98-digit number)

58832612208573370091…50106719388286320641

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

1.176 × 10⁹⁸(99-digit number)

11766522441714674018…00213438776572641279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.176 × 10⁹⁸(99-digit number)

11766522441714674018…00213438776572641281

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

2.353 × 10⁹⁸(99-digit number)

23533044883429348036…00426877553145282559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.353 × 10⁹⁸(99-digit number)

23533044883429348036…00426877553145282561

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

4.706 × 10⁹⁸(99-digit number)

47066089766858696073…00853755106290565119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.706 × 10⁹⁸(99-digit number)

47066089766858696073…00853755106290565121

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

9.413 × 10⁹⁸(99-digit number)

94132179533717392146…01707510212581130239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.413 × 10⁹⁸(99-digit number)

94132179533717392146…01707510212581130241

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

1.882 × 10⁹⁹(100-digit number)

18826435906743478429…03415020425162260479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,646,332

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