Block #2,813,003

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/28/2018, 12:25:39 AM · Difficulty 11.6754 · 4,031,435 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c260791c904609884e542b4493d58c634ff1d39af036fc39c53302f41e4afe82

View on Chainz ↗

Height

#2,813,003

Difficulty

11.675360

Transactions

Size

1.14 KB

Version

Bits

0bace46c

Nonce

14,681,991

Timestamp

8/28/2018, 12:25:39 AM

Confirmations

4,031,435

Mined by

⛏️ P2SHAbHWEc4NBvCdT6jgPZbsY3xZPMKotbBmfU

Merkle Root

2de095479417f66802860d2de39d4d280ea317a3b633acd063ef4edbc687f784

Transactions (2)

Coinbasedfbcbfe7b4aab3…873f4ebb38eedf

1 in → 1 out7.3300 XPM110 B

AbHWEc4N…KotbBmfU

695ffd7d00cfee…46729ad60586a1

6 in → 2 out5385.0487 XPM965 B

AMRycWoF…13hkF5ou AWbcPz2k…gJi82ADL

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.

7.909 × 10⁹⁵(96-digit number)

79099692368543797140…20980408441935544319

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

7.909 × 10⁹⁵(96-digit number)

79099692368543797140…20980408441935544319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.909 × 10⁹⁵(96-digit number)

79099692368543797140…20980408441935544321

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

1.581 × 10⁹⁶(97-digit number)

15819938473708759428…41960816883871088639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.581 × 10⁹⁶(97-digit number)

15819938473708759428…41960816883871088641

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

3.163 × 10⁹⁶(97-digit number)

31639876947417518856…83921633767742177279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.163 × 10⁹⁶(97-digit number)

31639876947417518856…83921633767742177281

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

6.327 × 10⁹⁶(97-digit number)

63279753894835037712…67843267535484354559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.327 × 10⁹⁶(97-digit number)

63279753894835037712…67843267535484354561

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

1.265 × 10⁹⁷(98-digit number)

12655950778967007542…35686535070968709119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.265 × 10⁹⁷(98-digit number)

12655950778967007542…35686535070968709121

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

2.531 × 10⁹⁷(98-digit number)

25311901557934015085…71373070141937418239

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 #2,813,003

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