Block #1,534,416

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 5:30:32 AM · Difficulty 10.6178 · 5,283,556 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a273b16162c750f888e237ae89cc187a944c7fa1aaf89655b11d3d56d9870ea

View on Chainz ↗

Height

#1,534,416

Difficulty

10.617841

Transactions

Size

21.60 KB

Version

Bits

0a9e2adb

Nonce

686,327,597

Timestamp

4/10/2016, 5:30:32 AM

Confirmations

5,283,556

Mined by

⛏️ P2SHAbJmcvEWbrMHAZXbgjo7cBf8T6r6uqa6QG

Merkle Root

6c8be84a8ea5f20085a120792e24420b16e5010e1be781beb96fdcfb2239b349

Transactions (4)

Coinbase5092c85aad2679…793216a8980930

1 in → 1 out9.0900 XPM109 B

AbJmcvEW…r6uqa6QG

9c5efed77be2c6…cad5e9f01f87fb

51 in → 1 out2736.7864 XPM7.42 KB

AUenGZEG…RXFZCYma

1fb313eaa9e1ac…f7bd08523ba1fd

45 in → 2 out371.1180 XPM6.57 KB

ASWppKUE…txmAPx5z AKmSu6ye…aQaXJ9uU

bbf464c628547d…3c7e3eead915c3

51 in → 1 out295.9197 XPM7.42 KB

AVud3sJ4…bEC87GXN

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.

8.152 × 10⁹⁵(96-digit number)

81522786282310755088…64057740723380689919

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

8.152 × 10⁹⁵(96-digit number)

81522786282310755088…64057740723380689919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.152 × 10⁹⁵(96-digit number)

81522786282310755088…64057740723380689921

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

1.630 × 10⁹⁶(97-digit number)

16304557256462151017…28115481446761379839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.630 × 10⁹⁶(97-digit number)

16304557256462151017…28115481446761379841

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

3.260 × 10⁹⁶(97-digit number)

32609114512924302035…56230962893522759679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.260 × 10⁹⁶(97-digit number)

32609114512924302035…56230962893522759681

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

6.521 × 10⁹⁶(97-digit number)

65218229025848604070…12461925787045519359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.521 × 10⁹⁶(97-digit number)

65218229025848604070…12461925787045519361

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

1.304 × 10⁹⁷(98-digit number)

13043645805169720814…24923851574091038719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.304 × 10⁹⁷(98-digit number)

13043645805169720814…24923851574091038721

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 #1,534,416

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