Block #2,666,055

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/18/2018, 12:42:37 AM · Difficulty 11.6649 · 4,173,145 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e38bab371ce4b1e4c41de4121fa844f6a860056dc688b0f92c3719e436650e23

View on Chainz ↗

Height

#2,666,055

Difficulty

11.664880

Transactions

Size

573 B

Version

Bits

0baa3592

Nonce

1,372,231,581

Timestamp

5/18/2018, 12:42:37 AM

Confirmations

4,173,145

Mined by

⛏️ P2SHAeP3mUrjSiBm9wSVzua1TnSrHW1QVYAWTD

Merkle Root

84df8ef208d604c364b53e7540601efc7bb439ba6d15721766e7a9e4b2c9b6e0

Transactions (2)

Coinbase2474736246e17c…28ca0c2bb16b78

1 in → 1 out7.3500 XPM109 B

AeP3mUrj…1QVYAWTD

4fc7d412e8df25…b70040e5548abd

2 in → 2 out850.0001 XPM373 B

AdiuyX4T…hhnR8fdD AXwvUvXg…ppeXMpXT

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.

8.443 × 10⁹⁵(96-digit number)

84434121205814685973…61660767199707684479

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

8.443 × 10⁹⁵(96-digit number)

84434121205814685973…61660767199707684479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.443 × 10⁹⁵(96-digit number)

84434121205814685973…61660767199707684481

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

1.688 × 10⁹⁶(97-digit number)

16886824241162937194…23321534399415368959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.688 × 10⁹⁶(97-digit number)

16886824241162937194…23321534399415368961

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

3.377 × 10⁹⁶(97-digit number)

33773648482325874389…46643068798830737919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.377 × 10⁹⁶(97-digit number)

33773648482325874389…46643068798830737921

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

6.754 × 10⁹⁶(97-digit number)

67547296964651748778…93286137597661475839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.754 × 10⁹⁶(97-digit number)

67547296964651748778…93286137597661475841

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

1.350 × 10⁹⁷(98-digit number)

13509459392930349755…86572275195322951679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.350 × 10⁹⁷(98-digit number)

13509459392930349755…86572275195322951681

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

2.701 × 10⁹⁷(98-digit number)

27018918785860699511…73144550390645903359

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 #2,666,055

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