Block #1,528,851

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2016, 10:04:07 AM · Difficulty 10.6113 · 5,298,161 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

35fa942667216116ad2de20666e5648c78f2e25c16e153b392b9eda5ca05fd1e

View on Chainz ↗

Height

#1,528,851

Difficulty

10.611307

Transactions

Size

1.18 KB

Version

Bits

0a9c7e9c

Nonce

72,526,477

Timestamp

4/6/2016, 10:04:07 AM

Confirmations

5,298,161

Mined by

⛏️ P2SHAbuh4nw9cRyHtGTw1NdZBkyPuAY73RMV7a

Merkle Root

0b75eb1916599b4776d7907c08a1edbb072297585200e52766bc8afb57eb163d

Transactions (2)

Coinbased41bc22c04d4da…0ec68ebc8c0350

1 in → 1 out8.8900 XPM110 B

Abuh4nw9…Y73RMV7a

4aeb5442ce71b1…78b2ee2e3e0534

1 in → 25 out200.0338 XPM1007 B

AVdytT8m…uTyJxvMD AbW1Qub6…fvcMNUTG ANJ1QmX9…khwkjshe AdyCMgJ3…on66hoS5 AVcSHYfC…DKv4QyN1

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.

1.422 × 10⁹⁵(96-digit number)

14222326371386391731…07361528096532593599

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

1.422 × 10⁹⁵(96-digit number)

14222326371386391731…07361528096532593599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.422 × 10⁹⁵(96-digit number)

14222326371386391731…07361528096532593601

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

2.844 × 10⁹⁵(96-digit number)

28444652742772783463…14723056193065187199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.844 × 10⁹⁵(96-digit number)

28444652742772783463…14723056193065187201

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

5.688 × 10⁹⁵(96-digit number)

56889305485545566926…29446112386130374399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.688 × 10⁹⁵(96-digit number)

56889305485545566926…29446112386130374401

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

1.137 × 10⁹⁶(97-digit number)

11377861097109113385…58892224772260748799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.137 × 10⁹⁶(97-digit number)

11377861097109113385…58892224772260748801

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

2.275 × 10⁹⁶(97-digit number)

22755722194218226770…17784449544521497599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.275 × 10⁹⁶(97-digit number)

22755722194218226770…17784449544521497601

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 #1,528,851

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