Block #1,383,383

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/24/2015, 8:09:58 PM · Difficulty 10.8090 · 5,443,693 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec95902f158bc3af9164ed349d369092bcfc24a4bd11db0b447af38787a68927

View on Chainz ↗

Height

#1,383,383

Difficulty

10.808998

Transactions

Size

1.01 KB

Version

Bits

0acf1a85

Nonce

1,727,055,521

Timestamp

12/24/2015, 8:09:58 PM

Confirmations

5,443,693

Mined by

⛏️ P2SHANvLzrWytjqXA6DdRjRN8YBAVUzLAMpCR8

Merkle Root

413832f7db77337487f8e21198ce987a8a6b4b4b93d3c470c7043aad341b8d5c

Transactions (2)

Coinbase9e52de159cf6ba…2f9846fed7f748

1 in → 1 out8.5600 XPM110 B

ANvLzrWy…zLAMpCR8

ae7e660dac46b4…440be522719512

1 in → 20 out178.9080 XPM838 B

AcZ2w3NH…5avstJwr AJxUiZXb…SLZYYGQ4 AKZ8dKSm…72z3gdjp AKjCtfjH…EZVn8gCd ASvFNRZd…brevmkjJ

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.

4.683 × 10⁹⁴(95-digit number)

46837713933226506643…65104424671405162039

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

4.683 × 10⁹⁴(95-digit number)

46837713933226506643…65104424671405162039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.683 × 10⁹⁴(95-digit number)

46837713933226506643…65104424671405162041

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

9.367 × 10⁹⁴(95-digit number)

93675427866453013287…30208849342810324079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.367 × 10⁹⁴(95-digit number)

93675427866453013287…30208849342810324081

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

1.873 × 10⁹⁵(96-digit number)

18735085573290602657…60417698685620648159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.873 × 10⁹⁵(96-digit number)

18735085573290602657…60417698685620648161

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

3.747 × 10⁹⁵(96-digit number)

37470171146581205314…20835397371241296319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.747 × 10⁹⁵(96-digit number)

37470171146581205314…20835397371241296321

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

7.494 × 10⁹⁵(96-digit number)

74940342293162410629…41670794742482592639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.494 × 10⁹⁵(96-digit number)

74940342293162410629…41670794742482592641

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 #1,383,383

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