Block #2,745,811

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/12/2018, 2:31:00 PM · Difficulty 11.6490 · 4,097,314 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

06138e812c072af4f148ed03957d6325e4e68f04d21042f4ef0b20c6c351e154

View on Chainz ↗

Height

#2,745,811

Difficulty

11.648977

Transactions

Size

2.43 KB

Version

Bits

0ba62363

Nonce

391,784,724

Timestamp

7/12/2018, 2:31:00 PM

Confirmations

4,097,314

Mined by

⛏️ P2SHAKxdetHw1DahWDMryud6C3w1HRwYvU3amS

Merkle Root

85aeed8f4bf0c08f67da3d979a69360f52b091bd562d5283d3501b045c3b05d6

Transactions (2)

Coinbase37b7379c805392…4ca68680579158

1 in → 1 out7.3900 XPM110 B

AKxdetHw…wYvU3amS

e7bdd7d1e7f35d…75073320a80cce

15 in → 2 out250.0474 XPM2.24 KB

AJcDB81D…ZX2on3Cs AY5rsAdT…qzb4AdDL

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.

1.374 × 10⁹⁶(97-digit number)

13743337624128747956…98563804470656051199

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

1.374 × 10⁹⁶(97-digit number)

13743337624128747956…98563804470656051199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.374 × 10⁹⁶(97-digit number)

13743337624128747956…98563804470656051201

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

2.748 × 10⁹⁶(97-digit number)

27486675248257495912…97127608941312102399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.748 × 10⁹⁶(97-digit number)

27486675248257495912…97127608941312102401

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

5.497 × 10⁹⁶(97-digit number)

54973350496514991825…94255217882624204799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.497 × 10⁹⁶(97-digit number)

54973350496514991825…94255217882624204801

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

1.099 × 10⁹⁷(98-digit number)

10994670099302998365…88510435765248409599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.099 × 10⁹⁷(98-digit number)

10994670099302998365…88510435765248409601

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

2.198 × 10⁹⁷(98-digit number)

21989340198605996730…77020871530496819199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.198 × 10⁹⁷(98-digit number)

21989340198605996730…77020871530496819201

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

4.397 × 10⁹⁷(98-digit number)

43978680397211993460…54041743060993638399

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 #2,745,811

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