Block #51,330

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 5:18:15 AM · Difficulty 8.8968 · 6,747,982 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c761061d526db2c59d52eb4dabb8fcf3176cb327e3ed53c2196a6e338c91c463

View on Chainz ↗

Height

#51,330

Difficulty

8.896837

Transactions

Size

1.06 KB

Version

Bits

08e5971a

Nonce

291

Timestamp

7/16/2013, 5:18:15 AM

Confirmations

6,747,982

Mined by

⛏️ P2SHAZEsi4F51CkJYAANhTvfs5aTmuRoFTR9EM

Merkle Root

7539b87940bf58251b8d8b96f27bcae55e66a467612ab94360c8e4dabbcf3cc4

Transactions (3)

Coinbasec6529a86fbe1ec…51f777540d7c97

1 in → 1 out12.6400 XPM110 B

AZEsi4F5…RoFTR9EM

e8a703365936d8…d88889df9c0d9c

6 in → 1 out79.3900 XPM726 B

ANoK3zJw…j7x2gmJP

50663f15e715f6…9843d5f5f010dc

1 in → 1 out12.8000 XPM158 B

AQF7TMJx…tCk9Eaar

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.

1.633 × 10¹⁰⁰(101-digit number)

16332299891171933861…56829305730822083919

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

1.633 × 10¹⁰⁰(101-digit number)

16332299891171933861…56829305730822083919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.633 × 10¹⁰⁰(101-digit number)

16332299891171933861…56829305730822083921

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

3.266 × 10¹⁰⁰(101-digit number)

32664599782343867723…13658611461644167839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.266 × 10¹⁰⁰(101-digit number)

32664599782343867723…13658611461644167841

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

6.532 × 10¹⁰⁰(101-digit number)

65329199564687735447…27317222923288335679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.532 × 10¹⁰⁰(101-digit number)

65329199564687735447…27317222923288335681

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

1.306 × 10¹⁰¹(102-digit number)

13065839912937547089…54634445846576671359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.306 × 10¹⁰¹(102-digit number)

13065839912937547089…54634445846576671361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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