Block #2,863,408

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/2/2018, 1:05:40 AM · Difficulty 11.6749 · 3,976,055 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9bcfa98ce51698f84f7c24dc96474a0fad53fb6be5dabcee45b77c7ad776ecd5

View on Chainz ↗

Height

#2,863,408

Difficulty

11.674902

Transactions

Size

868 B

Version

Bits

0bacc664

Nonce

1,464,420,050

Timestamp

10/2/2018, 1:05:40 AM

Confirmations

3,976,055

Mined by

⛏️ P2SHAGLtkToeMFsKiTK9UCtcNHDR4budDUwqkf

Merkle Root

6dfdb070463f8e57cda35cf2d65b1f455614f64206a7a039cb4c2bf5b0d20ea0

Transactions (2)

Coinbase0ce36dac191dac…72faffd4cb5469

1 in → 1 out7.3300 XPM110 B

AGLtkToe…udDUwqkf

0a304f06180430…015b8694e51f4c

4 in → 2 out649.0965 XPM668 B

AQmjqzoU…5U6sbve9 AYm2FgMq…GMfbnbn6

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.

6.167 × 10⁹⁴(95-digit number)

61670599794418537813…73228138714105359199

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

6.167 × 10⁹⁴(95-digit number)

61670599794418537813…73228138714105359199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.167 × 10⁹⁴(95-digit number)

61670599794418537813…73228138714105359201

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

1.233 × 10⁹⁵(96-digit number)

12334119958883707562…46456277428210718399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.233 × 10⁹⁵(96-digit number)

12334119958883707562…46456277428210718401

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

2.466 × 10⁹⁵(96-digit number)

24668239917767415125…92912554856421436799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.466 × 10⁹⁵(96-digit number)

24668239917767415125…92912554856421436801

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

4.933 × 10⁹⁵(96-digit number)

49336479835534830251…85825109712842873599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.933 × 10⁹⁵(96-digit number)

49336479835534830251…85825109712842873601

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

9.867 × 10⁹⁵(96-digit number)

98672959671069660502…71650219425685747199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.867 × 10⁹⁵(96-digit number)

98672959671069660502…71650219425685747201

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

1.973 × 10⁹⁶(97-digit number)

19734591934213932100…43300438851371494399

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 #2,863,408

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