Block #275,455

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 5:18:32 PM · Difficulty 9.9608 · 6,567,329 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

62fd95824af662ab92166b722eac4b6fbb7b36f88101f4726d54f4cca75462d5

View on Chainz ↗

Height

#275,455

Difficulty

9.960819

Transactions

Size

428 B

Version

Bits

09f5f838

Nonce

7,851

Timestamp

11/26/2013, 5:18:32 PM

Confirmations

6,567,329

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

23b43649b52ede8af96d01a0c92b1872a564f4e98a2296b447b2437476c9ea2a

Transactions (2)

Coinbasef68d9878377762…5f8af83aa50845

1 in → 2 out10.0700 XPM142 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

844f2132307384…69b7fb1fdaf876

1 in → 1 out0.3390 XPM193 B

Aa5nMYs6…x7kFV5Fq

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.

2.059 × 10¹⁰²(103-digit number)

20598668528556093152…79171657462202269949

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

2.059 × 10¹⁰²(103-digit number)

20598668528556093152…79171657462202269949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.059 × 10¹⁰²(103-digit number)

20598668528556093152…79171657462202269951

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

4.119 × 10¹⁰²(103-digit number)

41197337057112186305…58343314924404539899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.119 × 10¹⁰²(103-digit number)

41197337057112186305…58343314924404539901

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

8.239 × 10¹⁰²(103-digit number)

82394674114224372611…16686629848809079799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.239 × 10¹⁰²(103-digit number)

82394674114224372611…16686629848809079801

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

1.647 × 10¹⁰³(104-digit number)

16478934822844874522…33373259697618159599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.647 × 10¹⁰³(104-digit number)

16478934822844874522…33373259697618159601

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

3.295 × 10¹⁰³(104-digit number)

32957869645689749044…66746519395236319199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #275,455

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