Block #47,936

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 1:05:50 PM · Difficulty 8.8331 · 6,743,183 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5f5f04a5ae0dd2f635099c53585469c53724831d6e21eaa8e7a8290834ff4b92

View on Chainz ↗

Height

#47,936

Difficulty

8.833063

Transactions

Size

201 B

Version

Bits

08d543a2

Nonce

1,077

Timestamp

7/15/2013, 1:05:50 PM

Confirmations

6,743,183

Merkle Root

5f2ade818f03103c22cff3d62b16ef69aff776140947c36c7dcb855bca15a91b

Transactions (1)

Coinbase5f2ade818f0310…cb855bca15a91b

1 in → 1 out12.8000 XPM109 B

AeTcmmqH…LrFchfe1

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.

7.217 × 10⁹⁹(100-digit number)

72175939094995007472…22318588299313330639

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

7.217 × 10⁹⁹(100-digit number)

72175939094995007472…22318588299313330639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.217 × 10⁹⁹(100-digit number)

72175939094995007472…22318588299313330641

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

1.443 × 10¹⁰⁰(101-digit number)

14435187818999001494…44637176598626661279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.443 × 10¹⁰⁰(101-digit number)

14435187818999001494…44637176598626661281

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

2.887 × 10¹⁰⁰(101-digit number)

28870375637998002989…89274353197253322559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.887 × 10¹⁰⁰(101-digit number)

28870375637998002989…89274353197253322561

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

5.774 × 10¹⁰⁰(101-digit number)

57740751275996005978…78548706394506645119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.774 × 10¹⁰⁰(101-digit number)

57740751275996005978…78548706394506645121

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