Block #2,659,468

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 5/13/2018, 4:20:13 PM · Difficulty 11.6423 · 4,181,841 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d20db57a02b5ecbdc563c377e1a4d0e35ffc020d5d2f05c56ca09c67fed7c46e

View on Chainz ↗

Height

#2,659,468

Difficulty

11.642350

Transactions

Size

721 B

Version

Bits

0ba47106

Nonce

955,109,054

Timestamp

5/13/2018, 4:20:13 PM

Confirmations

4,181,841

Mined by

⛏️ P2SHAVF2swxTBNZDK1zpW8fkaM7mpF9G6pf3Xq

Merkle Root

646b98d5f15fe84039efe740c26ca144095617fd54b38500b981c5f271012a1c

Transactions (2)

Coinbasef120383f2a3ae8…572429a38879c5

1 in → 1 out7.3900 XPM110 B

AVF2swxT…9G6pf3Xq

e7f116e807fa94…ff85051c36c942

3 in → 2 out70.7681 XPM520 B

ARiCKETi…ZN7ureSY AUxDHVPK…RCEhdJgF

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.

1.599 × 10⁹⁸(99-digit number)

15992300348320121805…64479580176599613439

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

1.599 × 10⁹⁸(99-digit number)

15992300348320121805…64479580176599613439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.599 × 10⁹⁸(99-digit number)

15992300348320121805…64479580176599613441

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

3.198 × 10⁹⁸(99-digit number)

31984600696640243610…28959160353199226879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.198 × 10⁹⁸(99-digit number)

31984600696640243610…28959160353199226881

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

6.396 × 10⁹⁸(99-digit number)

63969201393280487221…57918320706398453759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.396 × 10⁹⁸(99-digit number)

63969201393280487221…57918320706398453761

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

1.279 × 10⁹⁹(100-digit number)

12793840278656097444…15836641412796907519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.279 × 10⁹⁹(100-digit number)

12793840278656097444…15836641412796907521

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

2.558 × 10⁹⁹(100-digit number)

25587680557312194888…31673282825593815039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.558 × 10⁹⁹(100-digit number)

25587680557312194888…31673282825593815041

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

5.117 × 10⁹⁹(100-digit number)

51175361114624389777…63346565651187630079

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

5.117 × 10⁹⁹(100-digit number)

51175361114624389777…63346565651187630081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,659,468

Cookie Preferences