Block #2,795,290

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/15/2018, 3:54:16 PM · Difficulty 11.6797 · 4,048,613 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

72da0812402533d2c7b2f23aa62b26fc7ce1f0ba313a0e6e7b3b58f12526d5f4

View on Chainz ↗

Height

#2,795,290

Difficulty

11.679672

Transactions

Size

427 B

Version

Bits

0badff03

Nonce

825,044,185

Timestamp

8/15/2018, 3:54:16 PM

Confirmations

4,048,613

Mined by

⛏️ P2SHAPLsJxUJbKEGveCgpQppk8BvLXLv8dN4Wi

Merkle Root

895fa38839d3deb73f994070bba85406c71697803c76b3d7fbc9494f92d6067e

Transactions (2)

Coinbasec3db510ac0dd72…d447c174dde9a3

1 in → 1 out7.3300 XPM109 B

APLsJxUJ…Lv8dN4Wi

27993413fbab13…0bd98983e022a1

1 in → 2 out2458.6615 XPM227 B

AbBZ2YM1…DCnYV5bb APo23fqo…othcLKxk

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.

1.478 × 10⁹⁷(98-digit number)

14786237467244343430…53034054468758487039

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

1.478 × 10⁹⁷(98-digit number)

14786237467244343430…53034054468758487039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.478 × 10⁹⁷(98-digit number)

14786237467244343430…53034054468758487041

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

2.957 × 10⁹⁷(98-digit number)

29572474934488686860…06068108937516974079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.957 × 10⁹⁷(98-digit number)

29572474934488686860…06068108937516974081

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

5.914 × 10⁹⁷(98-digit number)

59144949868977373721…12136217875033948159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.914 × 10⁹⁷(98-digit number)

59144949868977373721…12136217875033948161

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

1.182 × 10⁹⁸(99-digit number)

11828989973795474744…24272435750067896319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.182 × 10⁹⁸(99-digit number)

11828989973795474744…24272435750067896321

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

2.365 × 10⁹⁸(99-digit number)

23657979947590949488…48544871500135792639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.365 × 10⁹⁸(99-digit number)

23657979947590949488…48544871500135792641

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

4.731 × 10⁹⁸(99-digit number)

47315959895181898977…97089743000271585279

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 #2,795,290

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