Block #2,679,702

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/27/2018, 4:58:05 AM · Difficulty 11.6927 · 4,128,334 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

be51888178fb0b9a5a49bdce99244651d55c0b8aae88f9486faed1ba66aee868

View on Chainz ↗

Height

#2,679,702

Difficulty

11.692714

Transactions

Size

1.71 KB

Version

Bits

0bb155b6

Nonce

259,509,857

Timestamp

5/27/2018, 4:58:05 AM

Confirmations

4,128,334

Mined by

⛏️ P2SHAeUFCSPB2U5LDUguyhr42BH9VrVTFopS9w

Merkle Root

8c68f17fbda631a227c19187b30f94f539c544b195bebd0adea0c4beee61ee8d

Transactions (2)

Coinbasee4e5ac8caea721…908ec702477176

1 in → 1 out7.3200 XPM109 B

AeUFCSPB…VTFopS9w

7c50cd96c2dc47…eda2f06e125c9c

10 in → 2 out135.6633 XPM1.52 KB

AXbkjKtU…bbu2XDF6 AUFa2Xwm…voDDPxXw

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.

1.154 × 10⁹²(93-digit number)

11548067117676374685…53969453173366957119

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

1.154 × 10⁹²(93-digit number)

11548067117676374685…53969453173366957119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.154 × 10⁹²(93-digit number)

11548067117676374685…53969453173366957121

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

2.309 × 10⁹²(93-digit number)

23096134235352749371…07938906346733914239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.309 × 10⁹²(93-digit number)

23096134235352749371…07938906346733914241

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

4.619 × 10⁹²(93-digit number)

46192268470705498742…15877812693467828479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.619 × 10⁹²(93-digit number)

46192268470705498742…15877812693467828481

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

9.238 × 10⁹²(93-digit number)

92384536941410997484…31755625386935656959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.238 × 10⁹²(93-digit number)

92384536941410997484…31755625386935656961

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

1.847 × 10⁹³(94-digit number)

18476907388282199496…63511250773871313919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.847 × 10⁹³(94-digit number)

18476907388282199496…63511250773871313921

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

3.695 × 10⁹³(94-digit number)

36953814776564398993…27022501547742627839

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 #2,679,702

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