Block #2,765,090

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/25/2018, 8:03:14 PM · Difficulty 11.6651 · 4,068,606 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

338f99dc79ae46afd71414fdd52073bc45c186a2bb910503d8a289f78dcfb247

View on Chainz ↗

Height

#2,765,090

Difficulty

11.665057

Transactions

Size

1.43 KB

Version

Bits

0baa412c

Nonce

1,630,447,416

Timestamp

7/25/2018, 8:03:14 PM

Confirmations

4,068,606

Mined by

⛏️ P2SHAWFitWFjf55aErw9RXEHvSTNEtCvRbcQpN

Merkle Root

7917959da151af6e494150c97985105ce26c8b3a882a846f96eef9c32c684967

Transactions (2)

Coinbase35c9298b61bce2…b5ff55fd6c0202

1 in → 1 out7.3600 XPM110 B

AWFitWFj…CvRbcQpN

7d1ed7f7dbbed4…207a09aa32a673

8 in → 2 out310.6647 XPM1.23 KB

AbiZw7N1…HPacQJfk Aeovgf5W…qTToNStm

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.

3.962 × 10⁹⁹(100-digit number)

39623626376225114247…94149452895877529599

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

3.962 × 10⁹⁹(100-digit number)

39623626376225114247…94149452895877529599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.962 × 10⁹⁹(100-digit number)

39623626376225114247…94149452895877529601

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

7.924 × 10⁹⁹(100-digit number)

79247252752450228495…88298905791755059199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.924 × 10⁹⁹(100-digit number)

79247252752450228495…88298905791755059201

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

1.584 × 10¹⁰⁰(101-digit number)

15849450550490045699…76597811583510118399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.584 × 10¹⁰⁰(101-digit number)

15849450550490045699…76597811583510118401

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

3.169 × 10¹⁰⁰(101-digit number)

31698901100980091398…53195623167020236799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.169 × 10¹⁰⁰(101-digit number)

31698901100980091398…53195623167020236801

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

6.339 × 10¹⁰⁰(101-digit number)

63397802201960182796…06391246334040473599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.339 × 10¹⁰⁰(101-digit number)

63397802201960182796…06391246334040473601

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

1.267 × 10¹⁰¹(102-digit number)

12679560440392036559…12782492668080947199

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 #2,765,090

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