Block #2,575,212

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2018, 3:57:09 AM · Difficulty 10.9955 · 4,267,398 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b7e43242b41adf7a05b4213a2b0310ed8128374b168c36c08c5f62a159ccd0ab

View on Chainz ↗

Height

#2,575,212

Difficulty

10.995466

Transactions

Size

1.45 KB

Version

Bits

0afed6e0

Nonce

1,014,021,598

Timestamp

3/20/2018, 3:57:09 AM

Confirmations

4,267,398

Mined by

⛏️ P2SHAemnG2sniULt3cicWmS7Mfu3sLjbspDkWf

Merkle Root

9f603abeb7b95a3671d0c0de252cee23a0a6f4b6a804e9889b62f0b2e3954d05

Transactions (5)

Coinbaseb9c142d900d68d…f504d31a352b95

1 in → 1 out8.3000 XPM109 B

AemnG2sn…jbspDkWf

05cb93a2bc1ad6…4cffea1a854358

2 in → 2 out16.5100 XPM306 B

AS4wJ8cz…PMr3hhPv AewUD3fp…aoLJ7S34

bc6cdcaca35ff2…ca424d9059d4f7

2 in → 2 out16.5100 XPM305 B

ANSxzamF…7DSwsRrB AW3QZZmg…j2rGjUkp

ca0dfa5348880e…9347e2b55d0658

2 in → 2 out13.0400 XPM339 B

AYTwbyyw…mZr6wFJT AGAt263z…V1xVnord

28743c2a08b212…f03ea8327ae0d9

2 in → 2 out14.7900 XPM340 B

AR3cBEuE…9vc8keub AWRr3mx9…LVJ9qTsg

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.

5.274 × 10⁹⁵(96-digit number)

52745603018618916441…14630357918611799039

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

5.274 × 10⁹⁵(96-digit number)

52745603018618916441…14630357918611799039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.274 × 10⁹⁵(96-digit number)

52745603018618916441…14630357918611799041

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

1.054 × 10⁹⁶(97-digit number)

10549120603723783288…29260715837223598079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.054 × 10⁹⁶(97-digit number)

10549120603723783288…29260715837223598081

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

2.109 × 10⁹⁶(97-digit number)

21098241207447566576…58521431674447196159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.109 × 10⁹⁶(97-digit number)

21098241207447566576…58521431674447196161

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

4.219 × 10⁹⁶(97-digit number)

42196482414895133152…17042863348894392319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.219 × 10⁹⁶(97-digit number)

42196482414895133152…17042863348894392321

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

8.439 × 10⁹⁶(97-digit number)

84392964829790266305…34085726697788784639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.439 × 10⁹⁶(97-digit number)

84392964829790266305…34085726697788784641

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 #2,575,212

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