Block #294,260

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/4/2013, 6:57:49 PM · Difficulty 9.9909 · 6,508,903 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

82250f23dc8c582f6a95cc3297a8604b62c8bb4f57166206d62d7a116915749a

View on Chainz ↗

Height

#294,260

Difficulty

9.990940

Transactions

Size

1.14 KB

Version

Bits

09fdae39

Nonce

413

Timestamp

12/4/2013, 6:57:49 PM

Confirmations

6,508,903

Mined by

⛏️ t}aR{2AHuJ9wYhTJUvyVGtJfHi8VJT6eBGmgHrKZ

Merkle Root

424776438296ad6fd9559b9f1c97f1a35358381f6f87efabb54a9237af517f80

Transactions (1)

Coinbase424776438296ad…4a9237af517f80

1 in → 30 out9.9800 XPM1.06 KB

AHuJ9wYh…BGmgHrKZ AYcLTeXR…bscgPops AeX5uNnU…bNnowJSX AQyr8Lw3…hs4nt3Pn AUsdND2U…PxHWEPmG

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.

1.970 × 10⁹²(93-digit number)

19703994524705634018…50307237852935436799

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

1.970 × 10⁹²(93-digit number)

19703994524705634018…50307237852935436799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.970 × 10⁹²(93-digit number)

19703994524705634018…50307237852935436801

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

3.940 × 10⁹²(93-digit number)

39407989049411268036…00614475705870873599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.940 × 10⁹²(93-digit number)

39407989049411268036…00614475705870873601

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

7.881 × 10⁹²(93-digit number)

78815978098822536072…01228951411741747199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.881 × 10⁹²(93-digit number)

78815978098822536072…01228951411741747201

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

1.576 × 10⁹³(94-digit number)

15763195619764507214…02457902823483494399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.576 × 10⁹³(94-digit number)

15763195619764507214…02457902823483494401

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

3.152 × 10⁹³(94-digit number)

31526391239529014428…04915805646966988799

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