Block #1,534,795

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 11:44:01 AM · Difficulty 10.6182 · 5,283,164 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b7afbb4646660b2d77389f720da9085cae20ef2c425e29f5ef8ed0c4bfb043f9

View on Chainz ↗

Height

#1,534,795

Difficulty

10.618212

Transactions

Size

7.62 KB

Version

Bits

0a9e431d

Nonce

368,302,834

Timestamp

4/10/2016, 11:44:01 AM

Confirmations

5,283,164

Mined by

⛏️ P2SHAWDPoGqM8sVHHsz5o8r7ne7RASpamraruP

Merkle Root

5da552a77fae33d3a4be9b7c453d8c1adca11c4438a22e12770556ba0f2a932f

Transactions (2)

Coinbase5cde6ee97f836d…6eb18e5e1592f0

1 in → 1 out8.9400 XPM109 B

AWDPoGqM…pamraruP

f5d6918caf4f59…3350f4cc68a878

51 in → 1 out393.1153 XPM7.42 KB

AVr5qiJ9…HVa6bCrs

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.

1.717 × 10⁹⁸(99-digit number)

17174245323027506172…16044943720463564799

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

1.717 × 10⁹⁸(99-digit number)

17174245323027506172…16044943720463564799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.717 × 10⁹⁸(99-digit number)

17174245323027506172…16044943720463564801

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

3.434 × 10⁹⁸(99-digit number)

34348490646055012345…32089887440927129599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.434 × 10⁹⁸(99-digit number)

34348490646055012345…32089887440927129601

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

6.869 × 10⁹⁸(99-digit number)

68696981292110024691…64179774881854259199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.869 × 10⁹⁸(99-digit number)

68696981292110024691…64179774881854259201

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

1.373 × 10⁹⁹(100-digit number)

13739396258422004938…28359549763708518399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.373 × 10⁹⁹(100-digit number)

13739396258422004938…28359549763708518401

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

2.747 × 10⁹⁹(100-digit number)

27478792516844009876…56719099527417036799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.747 × 10⁹⁹(100-digit number)

27478792516844009876…56719099527417036801

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 #1,534,795

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