Block #2,577,185

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/21/2018, 5:38:57 AM · Difficulty 10.9959 · 4,264,128 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

105ca132be108086fb16bf1dd6b245da756c8969b39a3c7fa654049c911b5637

View on Chainz ↗

Height

#2,577,185

Difficulty

10.995895

Transactions

Size

846 B

Version

Bits

0afef2f7

Nonce

495,478,005

Timestamp

3/21/2018, 5:38:57 AM

Confirmations

4,264,128

Mined by

⛏️ P2SHAbQLSbSmkTVj7GN2P45P9deAE74o1EkQLA

Merkle Root

8ba1a57ea7de83189df145b8254ce5c941eb807889ec87eb43d983b168ee8642

Transactions (3)

Coinbase9a9bc9e21c9399…8e97660d0183c0

1 in → 1 out8.2800 XPM109 B

AbQLSbSm…4o1EkQLA

d6b219de9f4c69…89942a5dbe6d60

2 in → 2 out16.5100 XPM307 B

AKXYNWwm…xdwFMvjS AR3cBEuE…9vc8keub

ac29440f34052e…0436ca9a930014

2 in → 2 out14.7700 XPM339 B

ATW7AACe…3mh8DAsp AXxHU8uv…EKjx4i2F

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.

7.570 × 10⁹⁵(96-digit number)

75703126623969624678…28923677604016492799

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

7.570 × 10⁹⁵(96-digit number)

75703126623969624678…28923677604016492799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.570 × 10⁹⁵(96-digit number)

75703126623969624678…28923677604016492801

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

1.514 × 10⁹⁶(97-digit number)

15140625324793924935…57847355208032985599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.514 × 10⁹⁶(97-digit number)

15140625324793924935…57847355208032985601

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

3.028 × 10⁹⁶(97-digit number)

30281250649587849871…15694710416065971199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.028 × 10⁹⁶(97-digit number)

30281250649587849871…15694710416065971201

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

6.056 × 10⁹⁶(97-digit number)

60562501299175699742…31389420832131942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.056 × 10⁹⁶(97-digit number)

60562501299175699742…31389420832131942401

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

1.211 × 10⁹⁷(98-digit number)

12112500259835139948…62778841664263884799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.211 × 10⁹⁷(98-digit number)

12112500259835139948…62778841664263884801

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

2.422 × 10⁹⁷(98-digit number)

24225000519670279897…25557683328527769599

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 #2,577,185

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