Block #2,753,701

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/18/2018, 12:40:42 AM · Difficulty 11.6549 · 4,084,504 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fe1038a39ebf436f62b6ac906d666c3460b2f60984aac18c7a25280f372eedb9

View on Chainz ↗

Height

#2,753,701

Difficulty

11.654853

Transactions

Size

575 B

Version

Bits

0ba7a47a

Nonce

53,806,727

Timestamp

7/18/2018, 12:40:42 AM

Confirmations

4,084,504

Mined by

⛏️ P2SHAQqdfDZvzW1kRmcCHeYjeXsdYnR3qS3xzW

Merkle Root

cb6ffbdfdce5210072edacfdccef0da2f99fb6ff429face8f266ccc61eb06af9

Transactions (2)

Coinbasee2219d6ba00a24…ff8b3d17f0878f

1 in → 1 out7.3600 XPM110 B

AQqdfDZv…R3qS3xzW

554f428671233c…881dee0733a68a

2 in → 2 out2000.0104 XPM374 B

AbJJmNuT…5gHW4k3b 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.

2.897 × 10⁹⁷(98-digit number)

28978998544892121836…97909863997790822399

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

2.897 × 10⁹⁷(98-digit number)

28978998544892121836…97909863997790822399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.897 × 10⁹⁷(98-digit number)

28978998544892121836…97909863997790822401

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

5.795 × 10⁹⁷(98-digit number)

57957997089784243672…95819727995581644799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.795 × 10⁹⁷(98-digit number)

57957997089784243672…95819727995581644801

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

1.159 × 10⁹⁸(99-digit number)

11591599417956848734…91639455991163289599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.159 × 10⁹⁸(99-digit number)

11591599417956848734…91639455991163289601

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

2.318 × 10⁹⁸(99-digit number)

23183198835913697469…83278911982326579199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.318 × 10⁹⁸(99-digit number)

23183198835913697469…83278911982326579201

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

4.636 × 10⁹⁸(99-digit number)

46366397671827394938…66557823964653158399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.636 × 10⁹⁸(99-digit number)

46366397671827394938…66557823964653158401

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

9.273 × 10⁹⁸(99-digit number)

92732795343654789876…33115647929306316799

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 #2,753,701

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