Block #2,660,273

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/14/2018, 7:07:10 AM · Difficulty 11.6364 · 4,181,558 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3836ef216e22e4b1df9a0e0385c66a86da8b3d48010f597dbb766ade625ae468

View on Chainz ↗

Height

#2,660,273

Difficulty

11.636403

Transactions

Size

1.72 KB

Version

Bits

0ba2eb51

Nonce

2,045,022,408

Timestamp

5/14/2018, 7:07:10 AM

Confirmations

4,181,558

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

3f8c4339f1cb32427c109c9ab7e72b8c4811d3ff13134e54e581c577ebfd6931

Transactions (2)

Coinbase9d482a752032ce…d64046dae22a9c

1 in → 1 out7.3900 XPM110 B

Adqah8zh…1WwoHJ9t

d167b56147e1cc…0c2c87f9859d47

10 in → 2 out9889.8300 XPM1.52 KB

AJpDexog…6BDKEcEn ASULGtUR…1WyoKpVC

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.

6.375 × 10⁹⁷(98-digit number)

63753752729297923723…66292871703860787199

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

6.375 × 10⁹⁷(98-digit number)

63753752729297923723…66292871703860787199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.375 × 10⁹⁷(98-digit number)

63753752729297923723…66292871703860787201

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

1.275 × 10⁹⁸(99-digit number)

12750750545859584744…32585743407721574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.275 × 10⁹⁸(99-digit number)

12750750545859584744…32585743407721574401

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

2.550 × 10⁹⁸(99-digit number)

25501501091719169489…65171486815443148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.550 × 10⁹⁸(99-digit number)

25501501091719169489…65171486815443148801

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

5.100 × 10⁹⁸(99-digit number)

51003002183438338978…30342973630886297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.100 × 10⁹⁸(99-digit number)

51003002183438338978…30342973630886297601

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

1.020 × 10⁹⁹(100-digit number)

10200600436687667795…60685947261772595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.020 × 10⁹⁹(100-digit number)

10200600436687667795…60685947261772595201

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

2.040 × 10⁹⁹(100-digit number)

20401200873375335591…21371894523545190399

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 #2,660,273

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