Block #1,242,394

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/18/2015, 5:02:39 PM · Difficulty 10.7541 · 5,584,683 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a201863e82e03fb3bb11f0cf04fc4b724355f1c0d357acac4480c4a43fd77a52

View on Chainz ↗

Height

#1,242,394

Difficulty

10.754133

Transactions

Size

971 B

Version

Bits

0ac10ed8

Nonce

521,536,022

Timestamp

9/18/2015, 5:02:39 PM

Confirmations

5,584,683

Mined by

⛏️ P2SHALiVXamCNLmGdfhFAwnHHkE1YV5yeoT2k5

Merkle Root

08ede97f7d9eb8d83f1b92da4ec078e0244ee5568ca533c862e6a2888cc4ab04

Transactions (2)

Coinbase61e70d67d2134a…d7e928fefc0b87

1 in → 1 out8.6400 XPM110 B

ALiVXamC…5yeoT2k5

548808d9f9d1ba…b617ffb48db25d

1 in → 18 out205.8222 XPM771 B

AULskdRd…tq3PLuT4 AR8rqiUz…5Ng8ufwe AKUZ2tr9…Hct29YhT ANT6FYei…mwuM7Nif AT6Zeywt…nb8VCfee

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.

5.199 × 10⁹³(94-digit number)

51992512590417063545…80839742888532805119

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

5.199 × 10⁹³(94-digit number)

51992512590417063545…80839742888532805119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.199 × 10⁹³(94-digit number)

51992512590417063545…80839742888532805121

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

1.039 × 10⁹⁴(95-digit number)

10398502518083412709…61679485777065610239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.039 × 10⁹⁴(95-digit number)

10398502518083412709…61679485777065610241

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

2.079 × 10⁹⁴(95-digit number)

20797005036166825418…23358971554131220479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.079 × 10⁹⁴(95-digit number)

20797005036166825418…23358971554131220481

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

4.159 × 10⁹⁴(95-digit number)

41594010072333650836…46717943108262440959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.159 × 10⁹⁴(95-digit number)

41594010072333650836…46717943108262440961

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

8.318 × 10⁹⁴(95-digit number)

83188020144667301672…93435886216524881919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.318 × 10⁹⁴(95-digit number)

83188020144667301672…93435886216524881921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.663 × 10⁹⁵(96-digit number)

16637604028933460334…86871772433049763839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,242,394

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