Block #56,794

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/17/2013, 10:16:47 AM · Difficulty 8.9509 · 6,738,255 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

daf5c0ea8412c854bec55a5ec4c88819699d2c77c0c753c6dbf2450a28a9c2d2

View on Chainz ↗

Height

#56,794

Difficulty

8.950853

Transactions

Size

202 B

Version

Bits

08f36b19

Nonce

526

Timestamp

7/17/2013, 10:16:47 AM

Confirmations

6,738,255

Mined by

⛏️ P2SHAeTcmmqHMYEKBSfvTp4dmwQ4JaLrFchfe1

Merkle Root

ede0ff2c455fa8d919a18bd045b3eb323369f2434ab619fd969e1f41872888b8

Transactions (1)

Coinbaseede0ff2c455fa8…9e1f41872888b8

1 in → 1 out12.4600 XPM110 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.

1.502 × 10¹⁰⁰(101-digit number)

15023483242519753917…68463728445341775609

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

1.502 × 10¹⁰⁰(101-digit number)

15023483242519753917…68463728445341775609

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.502 × 10¹⁰⁰(101-digit number)

15023483242519753917…68463728445341775611

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

3.004 × 10¹⁰⁰(101-digit number)

30046966485039507835…36927456890683551219

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.004 × 10¹⁰⁰(101-digit number)

30046966485039507835…36927456890683551221

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

6.009 × 10¹⁰⁰(101-digit number)

60093932970079015670…73854913781367102439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.009 × 10¹⁰⁰(101-digit number)

60093932970079015670…73854913781367102441

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

1.201 × 10¹⁰¹(102-digit number)

12018786594015803134…47709827562734204879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.201 × 10¹⁰¹(102-digit number)

12018786594015803134…47709827562734204881

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