Block #455,440

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/22/2014, 1:45:55 PM · Difficulty 10.4101 · 6,354,123 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c51cdeff225c997927a84d50b86f8afef2c6d0182b4b2079e95e5b3875d55dc6

View on Chainz ↗

Height

#455,440

Difficulty

10.410109

Transactions

Size

2.41 KB

Version

Bits

0a68fcea

Nonce

11,600

Timestamp

3/22/2014, 1:45:55 PM

Confirmations

6,354,123

Mined by

⛏️ VAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

22e49ea40c651746dd97d73ccd40ac188a9dbf82e32094a6c2b270b30dc33ef6

Transactions (2)

Coinbasefb73cf0e00f518…8a09622720d4da

1 in → 23 out9.2300 XPM845 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AbHY4iza…Yckt2J5W AUzEPJFG…kYkA5U9V AbPcCMg4…719q6mAX

b28e7afbbc1be1…78f22b19066393

8 in → 15 out46.4513 XPM1.50 KB

AM36o72d…GrTCqp1H AMXcMroW…tUf9G3tY AXsvaFWm…Jy7HiavE AJrZAsFD…mqWWUUnE ASi6xQUs…69wHxuM7

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.

1.158 × 10⁹³(94-digit number)

11580727780521432271…59720394852083526509

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

1.158 × 10⁹³(94-digit number)

11580727780521432271…59720394852083526509

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.158 × 10⁹³(94-digit number)

11580727780521432271…59720394852083526511

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

2.316 × 10⁹³(94-digit number)

23161455561042864543…19440789704167053019

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.316 × 10⁹³(94-digit number)

23161455561042864543…19440789704167053021

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

4.632 × 10⁹³(94-digit number)

46322911122085729087…38881579408334106039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.632 × 10⁹³(94-digit number)

46322911122085729087…38881579408334106041

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

9.264 × 10⁹³(94-digit number)

92645822244171458175…77763158816668212079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.264 × 10⁹³(94-digit number)

92645822244171458175…77763158816668212081

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

1.852 × 10⁹⁴(95-digit number)

18529164448834291635…55526317633336424159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.852 × 10⁹⁴(95-digit number)

18529164448834291635…55526317633336424161

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

3.705 × 10⁹⁴(95-digit number)

37058328897668583270…11052635266672848319

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 #455,440

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