Block #49,199

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 7:04:30 PM · Difficulty 8.8605 · 6,761,385 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6b807e376ec87a76a19b74a7d70c50fec968a293b1fbc14bcb6cc598916252d8

View on Chainz ↗

Height

#49,199

Difficulty

8.860520

Transactions

Size

922 B

Version

Bits

08dc4b0d

Nonce

Timestamp

7/15/2013, 7:04:30 PM

Confirmations

6,761,385

Mined by

⛏️ P2SHAQ51E7uxJbrK6HnKcAZmn9fAGTfpRpWa62

Merkle Root

0956d66cd933beefc867bb3eb8fbbd97e4c5db9998f31b2db7be94bf21cae4af

Transactions (3)

Coinbased871c485fdc920…e55924a14bbc5b

1 in → 1 out12.7400 XPM110 B

AQ51E7ux…fpRpWa62

fad6b7f02ae456…01d09feaff6f7c

3 in → 2 out500.0157 XPM524 B

ALxzEmD2…hmsCULKi AZs2B9yK…WiwWMrTz

41d26c01106492…c752f41c9b9fa6

1 in → 1 out0.0700 XPM192 B

AaEohaBT…bCFyFubV

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.

6.653 × 10¹⁰⁸(109-digit number)

66535691730184625628…01569515779216377999

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

6.653 × 10¹⁰⁸(109-digit number)

66535691730184625628…01569515779216377999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.653 × 10¹⁰⁸(109-digit number)

66535691730184625628…01569515779216378001

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

1.330 × 10¹⁰⁹(110-digit number)

13307138346036925125…03139031558432755999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.330 × 10¹⁰⁹(110-digit number)

13307138346036925125…03139031558432756001

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

2.661 × 10¹⁰⁹(110-digit number)

26614276692073850251…06278063116865511999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.661 × 10¹⁰⁹(110-digit number)

26614276692073850251…06278063116865512001

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

5.322 × 10¹⁰⁹(110-digit number)

53228553384147700502…12556126233731023999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.322 × 10¹⁰⁹(110-digit number)

53228553384147700502…12556126233731024001

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

Block #49,199

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