Block #2,403,896

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2017, 8:33:05 AM · Difficulty 10.8930 · 4,435,361 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d4ff86b0a79a33fb9e3d9c73bf713a1303614fabc9385f9b68665c63b2395f28

View on Chainz ↗

Height

#2,403,896

Difficulty

10.892999

Transactions

Size

426 B

Version

Bits

0ae49b91

Nonce

81,641,957

Timestamp

12/1/2017, 8:33:05 AM

Confirmations

4,435,361

Mined by

⛏️ P2SHAavpaznRm2AE4iR7FUwZevVqxW3uhDW5ab

Merkle Root

bfb642b5622c8d9febe1e91bc78bd2ec52bac8b2f21b691d4249e7b042c2e24b

Transactions (2)

Coinbase2ff5977909a005…46dd975d085dbf

1 in → 1 out8.4200 XPM109 B

AavpaznR…3uhDW5ab

9f2cf8200e3fe8…8af8bbfe1ca6ee

1 in → 2 out4.9782 XPM226 B

AauSNYP2…xptZzzwM AMSwaBdK…DKsnDYzw

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.

1.064 × 10⁹⁶(97-digit number)

10640447689162951891…65458673058952028159

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

1.064 × 10⁹⁶(97-digit number)

10640447689162951891…65458673058952028159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.064 × 10⁹⁶(97-digit number)

10640447689162951891…65458673058952028161

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

2.128 × 10⁹⁶(97-digit number)

21280895378325903782…30917346117904056319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.128 × 10⁹⁶(97-digit number)

21280895378325903782…30917346117904056321

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

4.256 × 10⁹⁶(97-digit number)

42561790756651807565…61834692235808112639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.256 × 10⁹⁶(97-digit number)

42561790756651807565…61834692235808112641

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

8.512 × 10⁹⁶(97-digit number)

85123581513303615131…23669384471616225279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.512 × 10⁹⁶(97-digit number)

85123581513303615131…23669384471616225281

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

1.702 × 10⁹⁷(98-digit number)

17024716302660723026…47338768943232450559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.702 × 10⁹⁷(98-digit number)

17024716302660723026…47338768943232450561

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 #2,403,896

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