Block #1,599,995

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/25/2016, 10:09:08 PM · Difficulty 10.6042 · 5,240,695 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

290a51c44f862947d4f947e834cf154a381c60b7dd0fa20569cc784ea2e53aec

View on Chainz ↗

Height

#1,599,995

Difficulty

10.604191

Transactions

Size

1.29 KB

Version

Bits

0a9aac45

Nonce

2,095,980,683

Timestamp

5/25/2016, 10:09:08 PM

Confirmations

5,240,695

Mined by

⛏️ iAPEtWMfQDV4ozp3UZSoT5Ac2wuz1yeM1GF

Merkle Root

8fd22fa4ad7ae8d04aa6e971d93d503af330c0d2f662dd80faf456d7de9bf2ff

Transactions (2)

Coinbase57c8aad8844bee…edaee7703edf65

1 in → 1 out8.9000 XPM93 B

APEtWMfQ…z1yeM1GF

59c096fd52df6c…d0304440720af2

1 in → 29 out306.7654 XPM1.12 KB

Ae47uMAh…wjusD6zm APZ4tF1Q…SyYNSBsH AeTxVsPD…WV44fypq AZfVKzyv…Udj2GoeB AcDJv2aB…FumMJ837

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.

3.203 × 10⁹⁵(96-digit number)

32036537500630644833…56571159191915724799

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

3.203 × 10⁹⁵(96-digit number)

32036537500630644833…56571159191915724799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.203 × 10⁹⁵(96-digit number)

32036537500630644833…56571159191915724801

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

6.407 × 10⁹⁵(96-digit number)

64073075001261289666…13142318383831449599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.407 × 10⁹⁵(96-digit number)

64073075001261289666…13142318383831449601

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

1.281 × 10⁹⁶(97-digit number)

12814615000252257933…26284636767662899199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.281 × 10⁹⁶(97-digit number)

12814615000252257933…26284636767662899201

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

2.562 × 10⁹⁶(97-digit number)

25629230000504515866…52569273535325798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.562 × 10⁹⁶(97-digit number)

25629230000504515866…52569273535325798401

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

5.125 × 10⁹⁶(97-digit number)

51258460001009031733…05138547070651596799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.125 × 10⁹⁶(97-digit number)

51258460001009031733…05138547070651596801

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 #1,599,995

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