Block #2,242,880

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/8/2017, 7:21:17 PM · Difficulty 10.9474 · 4,588,817 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

13dfa3f29af9ee90636bcd6d1efc5dfa1e8e66b3d53c0f48a1225a8244f852cc

View on Chainz ↗

Height

#2,242,880

Difficulty

10.947433

Transactions

Size

869 B

Version

Bits

0af28aff

Nonce

589,181,354

Timestamp

8/8/2017, 7:21:17 PM

Confirmations

4,588,817

Mined by

⛏️ P2SHAUpF5EQHajWLzehSFv97rdN79VdHoJdqbi

Merkle Root

7bfd47a76daf6914346453bfcc3df506b2babf2e7b2f1c6ef34041028c9f9a3c

Transactions (2)

Coinbase46876fff2ded16…18424f3ad570c4

1 in → 1 out8.3400 XPM110 B

AUpF5EQH…dHoJdqbi

f3d839f1156922…7e22988839ca81

4 in → 2 out11671.4538 XPM669 B

AW74Hp5t…XdVQbbDE AG2iHzEk…eeZaDLVo

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.

3.229 × 10⁹⁵(96-digit number)

32292554455684931460…01078142491105196799

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

3.229 × 10⁹⁵(96-digit number)

32292554455684931460…01078142491105196799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.229 × 10⁹⁵(96-digit number)

32292554455684931460…01078142491105196801

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

6.458 × 10⁹⁵(96-digit number)

64585108911369862920…02156284982210393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.458 × 10⁹⁵(96-digit number)

64585108911369862920…02156284982210393601

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

1.291 × 10⁹⁶(97-digit number)

12917021782273972584…04312569964420787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.291 × 10⁹⁶(97-digit number)

12917021782273972584…04312569964420787201

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

2.583 × 10⁹⁶(97-digit number)

25834043564547945168…08625139928841574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.583 × 10⁹⁶(97-digit number)

25834043564547945168…08625139928841574401

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

5.166 × 10⁹⁶(97-digit number)

51668087129095890336…17250279857683148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.166 × 10⁹⁶(97-digit number)

51668087129095890336…17250279857683148801

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,242,880

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