Block #381,780

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/30/2014, 6:32:08 AM · Difficulty 10.4012 · 6,420,019 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dba17a2612325332d3abd0c401eee279f21c9dab09018bedd9f98331968881dd

View on Chainz ↗

Height

#381,780

Difficulty

10.401218

Transactions

Size

1.00 KB

Version

Bits

0a66b63b

Nonce

93,952

Timestamp

1/30/2014, 6:32:08 AM

Confirmations

6,420,019

Mined by

⛏️ TaRBAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

435f64681c349eceb2afe451d23e81db138abde2ad55df1865219a66e50aedab

Transactions (2)

Coinbasea43ae58f504773…b23d583ee44282

1 in → 21 out9.2300 XPM777 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH ANeHTs9o…oazVAG8Z AGQxR1oS…2N1xAZXN

962b821d464d55…1958809a7fb614

1 in → 1 out9.3400 XPM158 B

AbP1iY2S…QXTtEVYb

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.

4.889 × 10⁹⁴(95-digit number)

48894050776915134727…51037559460496390799

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

4.889 × 10⁹⁴(95-digit number)

48894050776915134727…51037559460496390799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.889 × 10⁹⁴(95-digit number)

48894050776915134727…51037559460496390801

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

9.778 × 10⁹⁴(95-digit number)

97788101553830269455…02075118920992781599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.778 × 10⁹⁴(95-digit number)

97788101553830269455…02075118920992781601

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

1.955 × 10⁹⁵(96-digit number)

19557620310766053891…04150237841985563199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.955 × 10⁹⁵(96-digit number)

19557620310766053891…04150237841985563201

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

3.911 × 10⁹⁵(96-digit number)

39115240621532107782…08300475683971126399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.911 × 10⁹⁵(96-digit number)

39115240621532107782…08300475683971126401

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

7.823 × 10⁹⁵(96-digit number)

78230481243064215564…16600951367942252799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.823 × 10⁹⁵(96-digit number)

78230481243064215564…16600951367942252801

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