Block #90,036

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 7:25:16 PM · Difficulty 9.2546 · 6,727,748 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86872c8f351e384d3abb540da3a0da229d2a049f8b8619843e5e5a251b047b86

View on Chainz ↗

Height

#90,036

Difficulty

9.254632

Transactions

Size

1.17 KB

Version

Bits

09412f98

Nonce

114,636

Timestamp

7/30/2013, 7:25:16 PM

Confirmations

6,727,748

Mined by

⛏️ P2SHAbBJHNdgp2rJLZzvJeeR1coko1vbdnytpU

Merkle Root

10288797a8d546993b87c4eee04a6b34fe14857ff463cf090424f62b65a3b9c8

Transactions (2)

Coinbase14dd4c1844680d…c622029d565c40

1 in → 1 out11.6700 XPM109 B

AbBJHNdg…vbdnytpU

6fdf2a7127b8aa…5c0f6275d1c3da

8 in → 2 out115.3400 XPM990 B

AeUqTmzS…MZinkG8Z Ae1ecBfz…Vk8wJR54

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.

8.370 × 10¹⁰⁷(108-digit number)

83703692216065544043…18910368036487317099

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

8.370 × 10¹⁰⁷(108-digit number)

83703692216065544043…18910368036487317099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.370 × 10¹⁰⁷(108-digit number)

83703692216065544043…18910368036487317101

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

1.674 × 10¹⁰⁸(109-digit number)

16740738443213108808…37820736072974634199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.674 × 10¹⁰⁸(109-digit number)

16740738443213108808…37820736072974634201

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

3.348 × 10¹⁰⁸(109-digit number)

33481476886426217617…75641472145949268399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.348 × 10¹⁰⁸(109-digit number)

33481476886426217617…75641472145949268401

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

6.696 × 10¹⁰⁸(109-digit number)

66962953772852435234…51282944291898536799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.696 × 10¹⁰⁸(109-digit number)

66962953772852435234…51282944291898536801

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

1.339 × 10¹⁰⁹(110-digit number)

13392590754570487046…02565888583797073599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #90,036

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