Block #2,679,511

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/27/2018, 1:48:24 AM · Difficulty 11.6927 · 4,161,390 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8c692343fde98629b67806178487b8485506da1232263cad68802232e1c7b9de

View on Chainz ↗

Height

#2,679,511

Difficulty

11.692729

Transactions

Size

1.31 KB

Version

Bits

0bb156ab

Nonce

1,123,768,439

Timestamp

5/27/2018, 1:48:24 AM

Confirmations

4,161,390

Mined by

⛏️ P2SHAcgmQSdw6D1tfRExPwetKX5NJh6w1UmP4v

Merkle Root

d1d845ad0034796e9b69637ac5377f48dd6a64e9ee14eeb3e00bbf08bf48cba5

Transactions (4)

Coinbase683aa82655ff45…52512ce25d58d5

1 in → 1 out7.3300 XPM110 B

AcgmQSdw…6w1UmP4v

4d957400ff235a…71330dd69c0f6a

5 in → 2 out32.4091 XPM683 B

AWp4iAg7…FUBLEm8x AVPVkDGi…hRc1QFdz

0a9ff7843253b0…31980eb8839cd8

1 in → 2 out2.4938 XPM226 B

ALvrNVZd…WWVpyiCu ASvX3ptr…35u52qcV

ff9fd4e3ff7a2e…8cd5e6e65706d5

1 in → 2 out1.4216 XPM226 B

APveumRB…DNYtvSaQ AVPmz695…YLJvJ9b1

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.

3.018 × 10⁹⁸(99-digit number)

30184616855491406760…00497579067742617599

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

3.018 × 10⁹⁸(99-digit number)

30184616855491406760…00497579067742617599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.018 × 10⁹⁸(99-digit number)

30184616855491406760…00497579067742617601

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

6.036 × 10⁹⁸(99-digit number)

60369233710982813521…00995158135485235199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.036 × 10⁹⁸(99-digit number)

60369233710982813521…00995158135485235201

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

1.207 × 10⁹⁹(100-digit number)

12073846742196562704…01990316270970470399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.207 × 10⁹⁹(100-digit number)

12073846742196562704…01990316270970470401

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

2.414 × 10⁹⁹(100-digit number)

24147693484393125408…03980632541940940799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.414 × 10⁹⁹(100-digit number)

24147693484393125408…03980632541940940801

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

4.829 × 10⁹⁹(100-digit number)

48295386968786250817…07961265083881881599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.829 × 10⁹⁹(100-digit number)

48295386968786250817…07961265083881881601

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

9.659 × 10⁹⁹(100-digit number)

96590773937572501634…15922530167763763199

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 #2,679,511

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