Block #90,152

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 9:39:12 PM · Difficulty 9.2518 · 6,699,707 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

59a6c311bd119b73ce55157102193b5f970e41a398e91961469a211151f77d3f

View on Chainz ↗

Height

#90,152

Difficulty

9.251837

Transactions

Size

206 B

Version

Bits

0940785e

Nonce

3,137

Timestamp

7/30/2013, 9:39:12 PM

Confirmations

6,699,707

Merkle Root

6ef1ea4fa9c0bf4f7cfbfc5938e37699bd4f468a25148b3c378a582e58a1b48e

Transactions (1)

Coinbase6ef1ea4fa9c0bf…8a582e58a1b48e

1 in → 1 out11.6700 XPM109 B

AK1JUKWL…oPR4rN5o

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.

7.357 × 10¹¹⁰(111-digit number)

73575913633377506834…04250286398390024199

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

7.357 × 10¹¹⁰(111-digit number)

73575913633377506834…04250286398390024199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.357 × 10¹¹⁰(111-digit number)

73575913633377506834…04250286398390024201

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

1.471 × 10¹¹¹(112-digit number)

14715182726675501366…08500572796780048399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.471 × 10¹¹¹(112-digit number)

14715182726675501366…08500572796780048401

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

2.943 × 10¹¹¹(112-digit number)

29430365453351002733…17001145593560096799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.943 × 10¹¹¹(112-digit number)

29430365453351002733…17001145593560096801

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

5.886 × 10¹¹¹(112-digit number)

58860730906702005467…34002291187120193599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.886 × 10¹¹¹(112-digit number)

58860730906702005467…34002291187120193601

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

1.177 × 10¹¹²(113-digit number)

11772146181340401093…68004582374240387199

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