Block #47,939

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 1:06:55 PM · Difficulty 8.8331 · 6,744,048 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7724f0f6089dbe4f4f323307cbd0dfade62f03efb4d0918e5e6f3ec6fcd4831b

View on Chainz ↗

Height

#47,939

Difficulty

8.833141

Transactions

Size

926 B

Version

Bits

08d548bd

Nonce

220

Timestamp

7/15/2013, 1:06:55 PM

Confirmations

6,744,048

Merkle Root

32729f905d50b361dd0e681f24cf3b47c2bc9fc55c55798cf7d0b8705448956d

Transactions (2)

Coinbase66951807621cd3…31d129f1965313

1 in → 1 out12.8100 XPM110 B

AGCUbq6M…QSxWg1oL

7eb8471fab2b06…46c8e64f6e6229

6 in → 1 out80.8400 XPM729 B

AQmtsowV…ixSa4vnc

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.

1.642 × 10⁸⁸(89-digit number)

16422781510322404165…70195854570639618879

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

1.642 × 10⁸⁸(89-digit number)

16422781510322404165…70195854570639618879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.642 × 10⁸⁸(89-digit number)

16422781510322404165…70195854570639618881

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

3.284 × 10⁸⁸(89-digit number)

32845563020644808330…40391709141279237759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.284 × 10⁸⁸(89-digit number)

32845563020644808330…40391709141279237761

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

6.569 × 10⁸⁸(89-digit number)

65691126041289616661…80783418282558475519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.569 × 10⁸⁸(89-digit number)

65691126041289616661…80783418282558475521

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

1.313 × 10⁸⁹(90-digit number)

13138225208257923332…61566836565116951039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.313 × 10⁸⁹(90-digit number)

13138225208257923332…61566836565116951041

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