Block #2,724,352

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/27/2018, 11:51:52 PM · Difficulty 11.6178 · 4,118,252 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

475956abbb666713cd122d26edc921fb7d8a5960d68e70f12b5d081ee2b47e44

View on Chainz ↗

Height

#2,724,352

Difficulty

11.617827

Transactions

Size

1.07 KB

Version

Bits

0b9e29e1

Nonce

622,878,244

Timestamp

6/27/2018, 11:51:52 PM

Confirmations

4,118,252

Mined by

⛏️ P2SHAVWiC4SxPyC6obEHg2XAopGA3KHHRdp7uT

Merkle Root

0f789899573a824f3f91e9e180eaf980215da6c3f946c65da0816f65f1be6a2c

Transactions (3)

Coinbasea73c56a4ec9721…a4df9c7dd90218

1 in → 1 out7.4200 XPM110 B

AVWiC4Sx…HHRdp7uT

36dab5db119238…41dceb92347be8

3 in → 2 out640.0099 XPM521 B

AQmjqzoU…5U6sbve9 AGTehdUY…z1TUh9yU

6cc63f3142e614…31d6afeeb6ab23

2 in → 2 out202.9197 XPM374 B

Aath4LCK…ij7FoGyC ATLw4wqX…kGTEjXFm

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.

1.763 × 10⁹⁵(96-digit number)

17639571647765620270…30637070855505223119

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

1.763 × 10⁹⁵(96-digit number)

17639571647765620270…30637070855505223119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.763 × 10⁹⁵(96-digit number)

17639571647765620270…30637070855505223121

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

3.527 × 10⁹⁵(96-digit number)

35279143295531240540…61274141711010446239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.527 × 10⁹⁵(96-digit number)

35279143295531240540…61274141711010446241

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

7.055 × 10⁹⁵(96-digit number)

70558286591062481081…22548283422020892479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.055 × 10⁹⁵(96-digit number)

70558286591062481081…22548283422020892481

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

1.411 × 10⁹⁶(97-digit number)

14111657318212496216…45096566844041784959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.411 × 10⁹⁶(97-digit number)

14111657318212496216…45096566844041784961

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

2.822 × 10⁹⁶(97-digit number)

28223314636424992432…90193133688083569919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.822 × 10⁹⁶(97-digit number)

28223314636424992432…90193133688083569921

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

5.644 × 10⁹⁶(97-digit number)

56446629272849984865…80386267376167139839

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 #2,724,352

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