Block #2,655,509

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/10/2018, 5:46:14 AM · Difficulty 11.7063 · 4,185,277 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e98908d0afbd14097d551a0ba986834903f352e89c6e1de5ce40a818f56e390f

View on Chainz ↗

Height

#2,655,509

Difficulty

11.706319

Transactions

Size

1.23 KB

Version

Bits

0bb4d150

Nonce

86,093,628

Timestamp

5/10/2018, 5:46:14 AM

Confirmations

4,185,277

Mined by

⛏️ P2SHAJv4gmuRyhyynLbwD7Mc7Ds8cWRPAzs3VZ

Merkle Root

c306ebc9fea66af1a443b6a06e5f441cf44b3282033e1a8ac9e5f2b82edf4ce8

Transactions (4)

Coinbased69fe9fef6ede6…7fbdc45df58e69

1 in → 1 out7.3100 XPM110 B

AJv4gmuR…RPAzs3VZ

d62bb9c10fb024…2935e0443271dd

1 in → 2 out7.2200 XPM193 B

AN7oKA8x…fmnTBgZA ASzWX3no…vdgq5yYM

c1a853d105721b…3af36802fb5bc9

1 in → 2 out7.2200 XPM191 B

AXAWWePq…U5yPY9rd ANxNfXmZ…4p5PaHCM

6f30857e39f13f…57d72df03d492b

4 in → 2 out0.1131 XPM672 B

ATknunA8…bi55VuPb AN7b55gz…YroqkbjU

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.

5.871 × 10⁹⁵(96-digit number)

58712282707181391605…11256831425391786719

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

5.871 × 10⁹⁵(96-digit number)

58712282707181391605…11256831425391786719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.871 × 10⁹⁵(96-digit number)

58712282707181391605…11256831425391786721

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

1.174 × 10⁹⁶(97-digit number)

11742456541436278321…22513662850783573439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.174 × 10⁹⁶(97-digit number)

11742456541436278321…22513662850783573441

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

2.348 × 10⁹⁶(97-digit number)

23484913082872556642…45027325701567146879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.348 × 10⁹⁶(97-digit number)

23484913082872556642…45027325701567146881

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

4.696 × 10⁹⁶(97-digit number)

46969826165745113284…90054651403134293759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.696 × 10⁹⁶(97-digit number)

46969826165745113284…90054651403134293761

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

9.393 × 10⁹⁶(97-digit number)

93939652331490226568…80109302806268587519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.393 × 10⁹⁶(97-digit number)

93939652331490226568…80109302806268587521

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

1.878 × 10⁹⁷(98-digit number)

18787930466298045313…60218605612537175039

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 #2,655,509

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