Block #294,930

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/5/2013, 4:06:43 AM · Difficulty 9.9912 · 6,516,122 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ae80c8d6b132682b748ae1a0953ed188535aeb7a2b3501a9ba61cc1489811cea

View on Chainz ↗

Height

#294,930

Difficulty

9.991178

Transactions

Size

1.75 KB

Version

Bits

09fdbdd6

Nonce

85,851

Timestamp

12/5/2013, 4:06:43 AM

Confirmations

6,516,122

Mined by

⛏️ aR{AHuJ9wYhTJUvyVGtJfHi8VJT6eBGmgHrKZ

Merkle Root

cac1a06ef513508ebb28b940283a71365f3d7fb5df218ee684c80bc3925a0bd1

Transactions (2)

Coinbase2bc068cf8fe126…74a0118d9ad16b

1 in → 30 out9.9800 XPM1.06 KB

AHuJ9wYh…BGmgHrKZ ARcqMJhp…RVLToQ6S AT5YHFNE…wEB3sX3V AKEwr54i…9BfmMkRh AReBFi8Q…Qq1cm1uS

277ba11b6ff61f…8cc039e6891e41

3 in → 7 out20.8591 XPM624 B

ATzgDXhL…oFbA8yH2 AUGXU3hL…Q9H3EpW2 AGQ2fgRV…bLy3QAAV AeKNrjNj…1NEq95Ta AKbpoask…dtBVWNrZ

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.

9.044 × 10⁹⁴(95-digit number)

90441624981794419689…17426954647278826879

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

9.044 × 10⁹⁴(95-digit number)

90441624981794419689…17426954647278826879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.044 × 10⁹⁴(95-digit number)

90441624981794419689…17426954647278826881

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

1.808 × 10⁹⁵(96-digit number)

18088324996358883937…34853909294557653759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.808 × 10⁹⁵(96-digit number)

18088324996358883937…34853909294557653761

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

3.617 × 10⁹⁵(96-digit number)

36176649992717767875…69707818589115307519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.617 × 10⁹⁵(96-digit number)

36176649992717767875…69707818589115307521

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

7.235 × 10⁹⁵(96-digit number)

72353299985435535751…39415637178230615039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.235 × 10⁹⁵(96-digit number)

72353299985435535751…39415637178230615041

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

1.447 × 10⁹⁶(97-digit number)

14470659997087107150…78831274356461230079

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 #294,930

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