Block #394,967

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2014, 8:25:05 AM · Difficulty 10.4195 · 6,431,782 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1e2741136e04c853967221365adac9b1ceeeab9fc109769838fc9c35fa5d11c0

View on Chainz ↗

Height

#394,967

Difficulty

10.419520

Transactions

Size

1.07 KB

Version

Bits

0a6b65aa

Nonce

279,576

Timestamp

2/8/2014, 8:25:05 AM

Confirmations

6,431,782

Mined by

⛏️ aRnAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f97b029a788cdeb8c9fa9657be5e546c2ec04b3479d39024a326020812476011

Transactions (2)

Coinbase5eda608272a070…f8ab67f14ae3ef

1 in → 21 out9.2000 XPM777 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AdV7BRAo…rTZPQMp1

42a632d7a16d0e…0bd01d17aabaa5

1 in → 2 out3.0718 XPM225 B

AVDEEJTZ…DkXe5mN3 ARSNDGqr…M8Q6JgC8

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.

7.253 × 10⁹⁸(99-digit number)

72538017849288228916…56844578062137210879

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

7.253 × 10⁹⁸(99-digit number)

72538017849288228916…56844578062137210879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.253 × 10⁹⁸(99-digit number)

72538017849288228916…56844578062137210881

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

1.450 × 10⁹⁹(100-digit number)

14507603569857645783…13689156124274421759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.450 × 10⁹⁹(100-digit number)

14507603569857645783…13689156124274421761

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

2.901 × 10⁹⁹(100-digit number)

29015207139715291566…27378312248548843519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.901 × 10⁹⁹(100-digit number)

29015207139715291566…27378312248548843521

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

5.803 × 10⁹⁹(100-digit number)

58030414279430583133…54756624497097687039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.803 × 10⁹⁹(100-digit number)

58030414279430583133…54756624497097687041

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

1.160 × 10¹⁰⁰(101-digit number)

11606082855886116626…09513248994195374079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.160 × 10¹⁰⁰(101-digit number)

11606082855886116626…09513248994195374081

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #394,967

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