Block #2,815,535

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/29/2018, 4:25:39 PM · Difficulty 11.6837 · 4,026,444 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b6c33348f51164b7173380152bfbb0ea5aaf0ff0a3daa127b8bb979dd9c07398

View on Chainz ↗

Height

#2,815,535

Difficulty

11.683729

Transactions

Size

1.64 KB

Version

Bits

0baf08d8

Nonce

751,582,268

Timestamp

8/29/2018, 4:25:39 PM

Confirmations

4,026,444

Mined by

⛏️ P2SHAK77Y7tYB71CsciXfFKvU9BfyWGoNugR6V

Merkle Root

a69410dc447ea1c4521239a223d053f7f24214e498b23a5c78103b47c513be02

Transactions (5)

Coinbasebf913dab899202…b9425dcc257950

1 in → 1 out7.3500 XPM110 B

AK77Y7tY…GoNugR6V

738008a9604a5d…efc1d82ed3505d

2 in → 2 out14.6500 XPM305 B

ATyjvTXU…scaPtq81 AM1oZyLd…efk8nevW

64db33da699319…ebc377aaadf3cc

2 in → 2 out14.6500 XPM306 B

ARnHDrKy…iSQnKD2W AVZY7fRQ…voPLHzeJ

9ad25eb7d02add…09834ba4778db9

2 in → 2 out11.9700 XPM341 B

APyCFc1B…MqweemEg APVKWthF…PMMxwRoz

1554fc560ae781…8b4f7ecc0b1852

3 in → 2 out10.6600 XPM522 B

AKo1Gi5i…wvzCbRvX APVKWthF…PMMxwRoz

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.

1.990 × 10⁹⁸(99-digit number)

19905856505242299409…61381415659302911999

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

1.990 × 10⁹⁸(99-digit number)

19905856505242299409…61381415659302911999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.990 × 10⁹⁸(99-digit number)

19905856505242299409…61381415659302912001

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

3.981 × 10⁹⁸(99-digit number)

39811713010484598819…22762831318605823999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.981 × 10⁹⁸(99-digit number)

39811713010484598819…22762831318605824001

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

7.962 × 10⁹⁸(99-digit number)

79623426020969197639…45525662637211647999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.962 × 10⁹⁸(99-digit number)

79623426020969197639…45525662637211648001

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

1.592 × 10⁹⁹(100-digit number)

15924685204193839527…91051325274423295999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.592 × 10⁹⁹(100-digit number)

15924685204193839527…91051325274423296001

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

3.184 × 10⁹⁹(100-digit number)

31849370408387679055…82102650548846591999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.184 × 10⁹⁹(100-digit number)

31849370408387679055…82102650548846592001

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

6.369 × 10⁹⁹(100-digit number)

63698740816775358111…64205301097693183999

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 #2,815,535

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