Block #292,317

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 4:05:15 PM · Difficulty 9.9903 · 6,522,760 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

37aa2115dcd909f2d8332820284a5d4b1f7a6c68de00e037a9e2a824cb62ebe1

View on Chainz ↗

Height

#292,317

Difficulty

9.990250

Transactions

Size

1.11 KB

Version

Bits

09fd810a

Nonce

124,871

Timestamp

12/3/2013, 4:05:15 PM

Confirmations

6,522,760

Mined by

⛏️ uaRaAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

08e26194a597a61ec892f9d853c9b58ce591a375bd6af44a3b59d2e79b9ffc2c

Transactions (1)

Coinbase08e26194a597a6…59d2e79b9ffc2c

1 in → 29 out9.9800 XPM1.02 KB

AZninDSu…FvgDMwC4 Ad9pSzHt…cpJ3y2zz ASXEwJrb…E3MLWChF ATSUeWML…N6kUrgvS Ac6mGvmQ…XqWmPHjR

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.

3.467 × 10⁹⁴(95-digit number)

34677330839543648135…74643665952448717119

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

3.467 × 10⁹⁴(95-digit number)

34677330839543648135…74643665952448717119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.467 × 10⁹⁴(95-digit number)

34677330839543648135…74643665952448717121

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

6.935 × 10⁹⁴(95-digit number)

69354661679087296270…49287331904897434239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.935 × 10⁹⁴(95-digit number)

69354661679087296270…49287331904897434241

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

1.387 × 10⁹⁵(96-digit number)

13870932335817459254…98574663809794868479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.387 × 10⁹⁵(96-digit number)

13870932335817459254…98574663809794868481

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

2.774 × 10⁹⁵(96-digit number)

27741864671634918508…97149327619589736959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.774 × 10⁹⁵(96-digit number)

27741864671634918508…97149327619589736961

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

5.548 × 10⁹⁵(96-digit number)

55483729343269837016…94298655239179473919

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 #292,317

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