Block #283,093

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 2:59:08 PM · Difficulty 9.9804 · 6,556,928 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86ca13c6aa7a191c034121276e99bd6922845d7823cab62a49465cb795b87330

View on Chainz ↗

Height

#283,093

Difficulty

9.980447

Transactions

Size

4.50 KB

Version

Bits

09fafe94

Nonce

42,691

Timestamp

11/29/2013, 2:59:08 PM

Confirmations

6,556,928

Mined by

⛏️ P2SHAPFoGEPx6aEwoQ7rmj1EAnbHxgNeCPiDDL

Merkle Root

a6aabb07b7a2208c085e4e205cb4082ce0b91a3447d9749bd01c929437c82310

Transactions (3)

Coinbasebe98b8a588657e…86a583fcd622d6

1 in → 1 out10.0700 XPM109 B

APFoGEPx…NeCPiDDL

08c94f2a681014…6e8bea699d8513

19 in → 1 out19.3609 XPM2.78 KB

AMpxNwqM…Q8UyocvD

e8bec1de77b33c…feda9339a05c5f

10 in → 2 out2.5192 XPM1.52 KB

AZ2qQVzc…3EzKSjah AVz2UE7J…nyt1Uy2c

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.

2.606 × 10⁸⁹(90-digit number)

26066000416459311697…35813819853110367119

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

2.606 × 10⁸⁹(90-digit number)

26066000416459311697…35813819853110367119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.606 × 10⁸⁹(90-digit number)

26066000416459311697…35813819853110367121

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

5.213 × 10⁸⁹(90-digit number)

52132000832918623395…71627639706220734239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.213 × 10⁸⁹(90-digit number)

52132000832918623395…71627639706220734241

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

1.042 × 10⁹⁰(91-digit number)

10426400166583724679…43255279412441468479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.042 × 10⁹⁰(91-digit number)

10426400166583724679…43255279412441468481

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

2.085 × 10⁹⁰(91-digit number)

20852800333167449358…86510558824882936959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.085 × 10⁹⁰(91-digit number)

20852800333167449358…86510558824882936961

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

4.170 × 10⁹⁰(91-digit number)

41705600666334898716…73021117649765873919

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 #283,093

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