Block #1,563,440

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/29/2016, 1:04:39 AM · Difficulty 10.7403 · 5,253,990 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4b0a8dbb9b15d46e732a033ae1a0f4a8ac03ab06f49377404ed13ef2f43b44e5

View on Chainz ↗

Height

#1,563,440

Difficulty

10.740310

Transactions

Size

832 B

Version

Bits

0abd84f7

Nonce

1,026,842,086

Timestamp

4/29/2016, 1:04:39 AM

Confirmations

5,253,990

Mined by

⛏️ P2SHAHqQNn2AKz3qTgpaqdW7SUXqssM2uUrttN

Merkle Root

744c3a3a9c5b6408bcda5faf0c33d67e0e8a7b5169fccdd3b5cee68b39cc700f

Transactions (2)

Coinbasec602d3584a888a…ab52050dd1ee3f

1 in → 1 out8.6700 XPM109 B

AHqQNn2A…M2uUrttN

2665fefa7e1d8c…be7914fc1c1ad8

1 in → 14 out228.8516 XPM634 B

AS8QLDvL…bhWUNELQ APCK2siw…tiEsULwz AUKMiWwK…QYx9bxGV ALW98R5z…DaBB37jw AdioeMWW…mbbMaHh7

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.

1.441 × 10⁹²(93-digit number)

14410768176303845921…57471279272275395679

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

1.441 × 10⁹²(93-digit number)

14410768176303845921…57471279272275395679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.441 × 10⁹²(93-digit number)

14410768176303845921…57471279272275395681

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

2.882 × 10⁹²(93-digit number)

28821536352607691843…14942558544550791359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.882 × 10⁹²(93-digit number)

28821536352607691843…14942558544550791361

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

5.764 × 10⁹²(93-digit number)

57643072705215383686…29885117089101582719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.764 × 10⁹²(93-digit number)

57643072705215383686…29885117089101582721

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

1.152 × 10⁹³(94-digit number)

11528614541043076737…59770234178203165439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.152 × 10⁹³(94-digit number)

11528614541043076737…59770234178203165441

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

2.305 × 10⁹³(94-digit number)

23057229082086153474…19540468356406330879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.305 × 10⁹³(94-digit number)

23057229082086153474…19540468356406330881

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 #1,563,440

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