Block #2,814,026

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 8/28/2018, 4:17:47 PM · Difficulty 11.6798 · 4,031,177 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ba3cf86397b12fcc1df135ba9312168f8086d39b0dbbd7b83ae343f3976076ba

View on Chainz ↗

Height

#2,814,026

Difficulty

11.679798

Transactions

Size

725 B

Version

Bits

0bae0739

Nonce

1,058,896,734

Timestamp

8/28/2018, 4:17:47 PM

Confirmations

4,031,177

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

ee4043ca99353bd083d86ca85c49fb2155bdde182e27c922dce5168657bccadc

Transactions (2)

Coinbase784736670dce7c…0fc581162980d0

1 in → 1 out7.3300 XPM110 B

AZtxQr2F…7grUWrUz

a040f4e21caa80…448332e5946d96

3 in → 2 out224.9086 XPM523 B

AMacMFhM…iFNVuut4 AX4bhuxW…FbHSuS6g

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.

1.200 × 10⁹⁹(100-digit number)

12002292709341840614…08260797253801738239

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

1.200 × 10⁹⁹(100-digit number)

12002292709341840614…08260797253801738239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.200 × 10⁹⁹(100-digit number)

12002292709341840614…08260797253801738241

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

2.400 × 10⁹⁹(100-digit number)

24004585418683681229…16521594507603476479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.400 × 10⁹⁹(100-digit number)

24004585418683681229…16521594507603476481

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

4.800 × 10⁹⁹(100-digit number)

48009170837367362458…33043189015206952959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.800 × 10⁹⁹(100-digit number)

48009170837367362458…33043189015206952961

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

9.601 × 10⁹⁹(100-digit number)

96018341674734724917…66086378030413905919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.601 × 10⁹⁹(100-digit number)

96018341674734724917…66086378030413905921

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

1.920 × 10¹⁰⁰(101-digit number)

19203668334946944983…32172756060827811839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.920 × 10¹⁰⁰(101-digit number)

19203668334946944983…32172756060827811841

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

3.840 × 10¹⁰⁰(101-digit number)

38407336669893889967…64345512121655623679

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

3.840 × 10¹⁰⁰(101-digit number)

38407336669893889967…64345512121655623681

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 #2,814,026

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