Block #1,588,326

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/17/2016, 9:08:26 AM · Difficulty 10.6501 · 5,225,826 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40007eacd4188769823d486be84db6fbc0b69a3185fab2ca2aa475cfd52d63d5

View on Chainz ↗

Height

#1,588,326

Difficulty

10.650094

Transactions

Size

1.25 KB

Version

Bits

0aa66c90

Nonce

618,390,501

Timestamp

5/17/2016, 9:08:26 AM

Confirmations

5,225,826

Mined by

⛏️ P2SHAeVkB9FkpPkckNQRQ5tYSwmtDpHXYEytGq

Merkle Root

25c92d8532fbca93bb794545ca06eec8827b7832a2283c603636e0c9cc7ebe88

Transactions (2)

Coinbase9988a4052e240d…938c9e4e64d9b5

1 in → 1 out8.8200 XPM109 B

AeVkB9Fk…HXYEytGq

7be4c796b3f4ee…38555a02aac814

1 in → 27 out19.8732 XPM1.05 KB

AVQ4ZAqT…i1UZixZ6 Aeh9MSYj…Y65xPQph AXRrPjHT…fY8pnmHW AJ3uRXtK…7TiTGTdo AYbps46k…SnM5TCdu

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.

3.033 × 10⁹⁴(95-digit number)

30337187649288767109…44096875212439093599

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

3.033 × 10⁹⁴(95-digit number)

30337187649288767109…44096875212439093599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.033 × 10⁹⁴(95-digit number)

30337187649288767109…44096875212439093601

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

6.067 × 10⁹⁴(95-digit number)

60674375298577534219…88193750424878187199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.067 × 10⁹⁴(95-digit number)

60674375298577534219…88193750424878187201

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

1.213 × 10⁹⁵(96-digit number)

12134875059715506843…76387500849756374399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.213 × 10⁹⁵(96-digit number)

12134875059715506843…76387500849756374401

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

2.426 × 10⁹⁵(96-digit number)

24269750119431013687…52775001699512748799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.426 × 10⁹⁵(96-digit number)

24269750119431013687…52775001699512748801

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

4.853 × 10⁹⁵(96-digit number)

48539500238862027375…05550003399025497599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.853 × 10⁹⁵(96-digit number)

48539500238862027375…05550003399025497601

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 #1,588,326

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