Block #2,594,758

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/1/2018, 1:54:17 AM · Difficulty 11.2992 · 4,247,425 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e587ee23de1e4281473a6bb26c94483f6c6d9bc52231f36aa6b6ccc3a2fe10fc

View on Chainz ↗

Height

#2,594,758

Difficulty

11.299243

Transactions

Size

812 B

Version

Bits

0b4c9b2f

Nonce

740,386,621

Timestamp

4/1/2018, 1:54:17 AM

Confirmations

4,247,425

Mined by

⛏️ P2SHAKhpq3J8YHyWNU7bmzNnDusbqrkp6hXQox

Merkle Root

4fca65c2489a351f7b1db54165296cca20d4a1e1f6c7714153ef05a3d26318be

Transactions (3)

Coinbasef03a7933f34531…00ffa9e357e8fa

1 in → 1 out7.8400 XPM110 B

AKhpq3J8…kp6hXQox

9713a668beeef1…4f7af8c8524df2

3 in → 2 out23.3600 XPM420 B

AWu6SVKR…fD2XKYmk ASVHn1RR…ZSBajeLN

9e535e2594fee6…8cb15464ad5703

1 in → 2 out7.7800 XPM192 B

AYGceJW4…pdtXAtdT AdxXry6p…3LAt843S

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.

1.271 × 10⁹⁵(96-digit number)

12714732400549611018…11712799250800168799

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

1.271 × 10⁹⁵(96-digit number)

12714732400549611018…11712799250800168799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.271 × 10⁹⁵(96-digit number)

12714732400549611018…11712799250800168801

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

2.542 × 10⁹⁵(96-digit number)

25429464801099222037…23425598501600337599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.542 × 10⁹⁵(96-digit number)

25429464801099222037…23425598501600337601

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

5.085 × 10⁹⁵(96-digit number)

50858929602198444075…46851197003200675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.085 × 10⁹⁵(96-digit number)

50858929602198444075…46851197003200675201

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

1.017 × 10⁹⁶(97-digit number)

10171785920439688815…93702394006401350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.017 × 10⁹⁶(97-digit number)

10171785920439688815…93702394006401350401

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

2.034 × 10⁹⁶(97-digit number)

20343571840879377630…87404788012802700799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.034 × 10⁹⁶(97-digit number)

20343571840879377630…87404788012802700801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.068 × 10⁹⁶(97-digit number)

40687143681758755260…74809576025605401599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,594,758

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