Block #1,516,766

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/29/2016, 2:13:05 AM · Difficulty 10.6032 · 5,279,642 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

63fb6b9eb65f18b5afdfbd8c6ac9e0db7c3bd189006d1cb2f0d05ec661a9fae0

View on Chainz ↗

Height

#1,516,766

Difficulty

10.603247

Transactions

Size

426 B

Version

Bits

0a9a6e5d

Nonce

1,023,437,805

Timestamp

3/29/2016, 2:13:05 AM

Confirmations

5,279,642

Mined by

⛏️ P2SHAR9iNGyRRu12jVpeBZaQ5jS9vx1TjuursL

Merkle Root

a3301062e53190f21b469e7459020f17d1352337333eb5ba512e1d2d2402dd21

Transactions (2)

Coinbase7aa9cb14d4812d…650dce96fab331

1 in → 1 out8.8900 XPM109 B

AR9iNGyR…1TjuursL

5fee52b0355990…72d82e7a2c9dc3

1 in → 2 out12973.6784 XPM226 B

AWbVLQFv…NfYzWqWQ AdZ82MdW…3aWky2BV

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.

1.555 × 10⁹⁸(99-digit number)

15552315398301896242…10544678040429199359

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

1.555 × 10⁹⁸(99-digit number)

15552315398301896242…10544678040429199359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.555 × 10⁹⁸(99-digit number)

15552315398301896242…10544678040429199361

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

3.110 × 10⁹⁸(99-digit number)

31104630796603792484…21089356080858398719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.110 × 10⁹⁸(99-digit number)

31104630796603792484…21089356080858398721

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

6.220 × 10⁹⁸(99-digit number)

62209261593207584968…42178712161716797439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.220 × 10⁹⁸(99-digit number)

62209261593207584968…42178712161716797441

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

1.244 × 10⁹⁹(100-digit number)

12441852318641516993…84357424323433594879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.244 × 10⁹⁹(100-digit number)

12441852318641516993…84357424323433594881

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

2.488 × 10⁹⁹(100-digit number)

24883704637283033987…68714848646867189759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.488 × 10⁹⁹(100-digit number)

24883704637283033987…68714848646867189761

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