Block #49,981

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 11:06:27 PM · Difficulty 8.8747 · 6,745,682 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cffad567b7c990120bc4b50777846c08326d96d6f1013f91646e3fa2d86ee12f

View on Chainz ↗

Height

#49,981

Difficulty

8.874726

Transactions

Size

845 B

Version

Bits

08dfee07

Nonce

238

Timestamp

7/15/2013, 11:06:27 PM

Confirmations

6,745,682

Mined by

⛏️ P2SHAcBadmkptMo3EwP8cg9ZUyqvJMGmhL921o

Merkle Root

172b252df7a2b2692aa902661ecf405cbdca3cffaa7b4164b295510e682f9422

Transactions (2)

Coinbaseb9c0a846a7145d…be80c7305734b2

1 in → 1 out12.6900 XPM110 B

AcBadmkp…GmhL921o

02b3a7f3b7dca5…80f804a74f1af1

4 in → 1 out2031.0000 XPM638 B

AMyN7uD8…6UvugCNh

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.

7.481 × 10¹¹⁰(111-digit number)

74817005949761416491…84027930446095483649

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

7.481 × 10¹¹⁰(111-digit number)

74817005949761416491…84027930446095483649

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.481 × 10¹¹⁰(111-digit number)

74817005949761416491…84027930446095483651

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

1.496 × 10¹¹¹(112-digit number)

14963401189952283298…68055860892190967299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.496 × 10¹¹¹(112-digit number)

14963401189952283298…68055860892190967301

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

2.992 × 10¹¹¹(112-digit number)

29926802379904566596…36111721784381934599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.992 × 10¹¹¹(112-digit number)

29926802379904566596…36111721784381934601

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

5.985 × 10¹¹¹(112-digit number)

59853604759809133193…72223443568763869199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.985 × 10¹¹¹(112-digit number)

59853604759809133193…72223443568763869201

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