Block #2,641,871

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 12:36:24 PM · Difficulty 11.6347 · 4,189,012 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

04a8dc30acfe7612b687532dcfe7c2563a7a78f4d5613d8a275d8ba674258d12

View on Chainz ↗

Height

#2,641,871

Difficulty

11.634746

Transactions

Size

1.22 KB

Version

Bits

0ba27eba

Nonce

939,684,340

Timestamp

5/1/2018, 12:36:24 PM

Confirmations

4,189,012

Mined by

⛏️ P2SHAU493J8XVNCDEt4z9U6WDiKhx7xjcDZVLe

Merkle Root

c4780a393d80f0baa7eaa1c5408392c27399f416dd600ffc3e9b78e7e409a803

Transactions (5)

Coinbase3bf6024281dc20…5be5fd8c637596

1 in → 1 out7.4100 XPM110 B

AU493J8X…xjcDZVLe

d1ad902c5ecd81…41f48127f691d2

1 in → 2 out2.6171 XPM226 B

AHwpSb4U…Nsp5hnCk AesZwffM…aqGftK5G

5d3bfa104b65c2…00eddb0a2c5051

1 in → 2 out2.4190 XPM226 B

ARJTFmXi…9mT6237k ATRC1AVA…sUk4VJvc

9ba1fc60ac311b…eb4f509a627013

1 in → 2 out0.1669 XPM226 B

AZBGBBQd…ExqEYGNc AHydNHEx…aEFz2JPY

567dd5b1ca522b…cc79609048007c

2 in → 2 out2.1440 XPM374 B

AJF3RxP5…GoF8KQUr APHuneyb…qtS4PMFv

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.

3.512 × 10⁹⁶(97-digit number)

35126434935607543666…32899065367405578239

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

3.512 × 10⁹⁶(97-digit number)

35126434935607543666…32899065367405578239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.512 × 10⁹⁶(97-digit number)

35126434935607543666…32899065367405578241

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

7.025 × 10⁹⁶(97-digit number)

70252869871215087333…65798130734811156479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.025 × 10⁹⁶(97-digit number)

70252869871215087333…65798130734811156481

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

1.405 × 10⁹⁷(98-digit number)

14050573974243017466…31596261469622312959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.405 × 10⁹⁷(98-digit number)

14050573974243017466…31596261469622312961

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

2.810 × 10⁹⁷(98-digit number)

28101147948486034933…63192522939244625919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.810 × 10⁹⁷(98-digit number)

28101147948486034933…63192522939244625921

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

5.620 × 10⁹⁷(98-digit number)

56202295896972069866…26385045878489251839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.620 × 10⁹⁷(98-digit number)

56202295896972069866…26385045878489251841

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

1.124 × 10⁹⁸(99-digit number)

11240459179394413973…52770091756978503679

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 #2,641,871

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