Block #2,646,066

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 4:40:39 AM · Difficulty 11.7441 · 4,190,287 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1d923c4cfc6025ac86f4da769f04238fa43c1f2a72e99d6e8d06a7d96100c9da

View on Chainz ↗

Height

#2,646,066

Difficulty

11.744106

Transactions

Size

3.02 KB

Version

Bits

0bbe7db4

Nonce

799,603,972

Timestamp

5/3/2018, 4:40:39 AM

Confirmations

4,190,287

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

02c351a96a55f68ec94a1b11d0b5275445520376945f74dd5d3bddb86ab7f47a

Transactions (2)

Coinbase9d764dbff60e2c…e17160b48e356c

1 in → 1 out7.2700 XPM109 B

Adqah8zh…1WwoHJ9t

b8fac7677c5bac…a8914e2a3a4911

19 in → 2 out142.1000 XPM2.82 KB

AFuSYUMc…AJufouvu ALjLjYzh…ehX7Jx55

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.

4.417 × 10⁹⁸(99-digit number)

44171400814270535106…74940369768250736639

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

4.417 × 10⁹⁸(99-digit number)

44171400814270535106…74940369768250736639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.417 × 10⁹⁸(99-digit number)

44171400814270535106…74940369768250736641

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

8.834 × 10⁹⁸(99-digit number)

88342801628541070212…49880739536501473279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.834 × 10⁹⁸(99-digit number)

88342801628541070212…49880739536501473281

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

1.766 × 10⁹⁹(100-digit number)

17668560325708214042…99761479073002946559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.766 × 10⁹⁹(100-digit number)

17668560325708214042…99761479073002946561

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

3.533 × 10⁹⁹(100-digit number)

35337120651416428085…99522958146005893119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.533 × 10⁹⁹(100-digit number)

35337120651416428085…99522958146005893121

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

7.067 × 10⁹⁹(100-digit number)

70674241302832856170…99045916292011786239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.067 × 10⁹⁹(100-digit number)

70674241302832856170…99045916292011786241

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

1.413 × 10¹⁰⁰(101-digit number)

14134848260566571234…98091832584023572479

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 #2,646,066

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