Block #2,667,138

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/18/2018, 5:41:30 PM · Difficulty 11.6692 · 4,164,799 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

300ae9c76042a43b4c8835213d2529bd6082ca9504932eaa8f5c42f552db8d89

View on Chainz ↗

Height

#2,667,138

Difficulty

11.669158

Transactions

Size

28.28 KB

Version

Bits

0bab4def

Nonce

375,960,796

Timestamp

5/18/2018, 5:41:30 PM

Confirmations

4,164,799

Mined by

⛏️ P2SHAMXQnrZtwTTmZXme8PiUf5jG2XxLutTLu4

Merkle Root

29cbd8f13040bc107932c4dfcd9373074a30771f31ef3b450e8a33069d5f8145

Transactions (2)

Coinbasebfa2a993e3076a…0aa0450399492f

1 in → 1 out7.6300 XPM110 B

AMXQnrZt…xLutTLu4

4431a316d98c17…675afdcd7069dc

195 in → 2 out121.0100 XPM28.08 KB

AK7Cw8FY…f65no6y7 AcprKFHC…D4cVWMLN

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.

4.575 × 10⁹⁷(98-digit number)

45753282955961366209…81507010071708139519

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

4.575 × 10⁹⁷(98-digit number)

45753282955961366209…81507010071708139519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.575 × 10⁹⁷(98-digit number)

45753282955961366209…81507010071708139521

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

9.150 × 10⁹⁷(98-digit number)

91506565911922732419…63014020143416279039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.150 × 10⁹⁷(98-digit number)

91506565911922732419…63014020143416279041

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

1.830 × 10⁹⁸(99-digit number)

18301313182384546483…26028040286832558079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.830 × 10⁹⁸(99-digit number)

18301313182384546483…26028040286832558081

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

3.660 × 10⁹⁸(99-digit number)

36602626364769092967…52056080573665116159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.660 × 10⁹⁸(99-digit number)

36602626364769092967…52056080573665116161

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

7.320 × 10⁹⁸(99-digit number)

73205252729538185935…04112161147330232319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.320 × 10⁹⁸(99-digit number)

73205252729538185935…04112161147330232321

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

1.464 × 10⁹⁹(100-digit number)

14641050545907637187…08224322294660464639

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 #2,667,138

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