Block #1,563,772

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/29/2016, 6:07:01 AM · Difficulty 10.7418 · 5,261,596 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2adad8bda52066150149a618192024ae04a962c65555608dc656f2df3e322883

View on Chainz ↗

Height

#1,563,772

Difficulty

10.741770

Transactions

Size

937 B

Version

Bits

0abde49f

Nonce

81,053,491

Timestamp

4/29/2016, 6:07:01 AM

Confirmations

5,261,596

Mined by

⛏️ P2SHASVxXQo9s8uzvK4SF23GoqcXQFQdGypV3E

Merkle Root

b91c9fa89249a5bca9274c390341c8347487ed4c4057b38ef47845d1b2054934

Transactions (2)

Coinbase26789280161d21…1cf6d63c22051f

1 in → 1 out8.6600 XPM110 B

ASVxXQo9…QdGypV3E

4c19b7d22a280a…d1e49174f54347

1 in → 17 out224.4923 XPM737 B

APkYqeDC…HdUtG6Vu AdFGzKVN…Uu1eQjFc ALZzJ9z8…qdGrQhTQ AX3mouNr…NAsScmbG AVymmZy7…LU5Rurin

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.

3.356 × 10⁹⁴(95-digit number)

33564509656350739235…34427456022625761359

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

3.356 × 10⁹⁴(95-digit number)

33564509656350739235…34427456022625761359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.356 × 10⁹⁴(95-digit number)

33564509656350739235…34427456022625761361

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

6.712 × 10⁹⁴(95-digit number)

67129019312701478470…68854912045251522719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.712 × 10⁹⁴(95-digit number)

67129019312701478470…68854912045251522721

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

1.342 × 10⁹⁵(96-digit number)

13425803862540295694…37709824090503045439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.342 × 10⁹⁵(96-digit number)

13425803862540295694…37709824090503045441

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

2.685 × 10⁹⁵(96-digit number)

26851607725080591388…75419648181006090879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.685 × 10⁹⁵(96-digit number)

26851607725080591388…75419648181006090881

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

5.370 × 10⁹⁵(96-digit number)

53703215450161182776…50839296362012181759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.370 × 10⁹⁵(96-digit number)

53703215450161182776…50839296362012181761

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 #1,563,772

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