Block #2,675,362

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/24/2018, 2:38:20 AM · Difficulty 11.6998 · 4,156,119 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c48e98afcd203905b8b54a841b112e271bee1c38bc7d7257d7e923841aacbd35

View on Chainz ↗

Height

#2,675,362

Difficulty

11.699792

Transactions

Size

951 B

Version

Bits

0bb3258d

Nonce

1,301,398,110

Timestamp

5/24/2018, 2:38:20 AM

Confirmations

4,156,119

Mined by

⛏️ P2SHAQAhbdZkR3tYQkPUrHjhvXed87ocTX7eey

Merkle Root

267b045e5db4cece89e89245fc2d1c6bad7a14c200d4bfe6bb41053ae3da5786

Transactions (3)

Coinbasebb550b18af59e9…7d36f019ad1dde

1 in → 1 out7.3100 XPM110 B

AQAhbdZk…ocTX7eey

1f84bdd357e21a…db470af2e332ff

1 in → 2 out19999.9900 XPM227 B

ALFCjDjB…XEfXtzaq Ab4vr4oq…AtM4C5HY

444a30bfdd8532…f45d8dcde3fcfd

3 in → 2 out11.3242 XPM524 B

AKW7c77U…RQZsRCGA AGhzcDHG…MZv6XCbm

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.

7.619 × 10⁹³(94-digit number)

76192844277744328939…26599617494131752959

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

7.619 × 10⁹³(94-digit number)

76192844277744328939…26599617494131752959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.619 × 10⁹³(94-digit number)

76192844277744328939…26599617494131752961

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

1.523 × 10⁹⁴(95-digit number)

15238568855548865787…53199234988263505919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.523 × 10⁹⁴(95-digit number)

15238568855548865787…53199234988263505921

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

3.047 × 10⁹⁴(95-digit number)

30477137711097731575…06398469976527011839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.047 × 10⁹⁴(95-digit number)

30477137711097731575…06398469976527011841

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

6.095 × 10⁹⁴(95-digit number)

60954275422195463151…12796939953054023679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.095 × 10⁹⁴(95-digit number)

60954275422195463151…12796939953054023681

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

1.219 × 10⁹⁵(96-digit number)

12190855084439092630…25593879906108047359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.219 × 10⁹⁵(96-digit number)

12190855084439092630…25593879906108047361

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

2.438 × 10⁹⁵(96-digit number)

24381710168878185260…51187759812216094719

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 #2,675,362

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