Block #28,300

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 11:49:47 AM · Difficulty 7.9815 · 6,770,722 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6cad1f9075f23717138f12692d07c40cf4ee3ec5eeebcfc5caf54d767a433db3

View on Chainz ↗

Height

#28,300

Difficulty

7.981520

Transactions

Size

199 B

Version

Bits

07fb44e7

Nonce

316

Timestamp

7/13/2013, 11:49:47 AM

Confirmations

6,770,722

Mined by

⛏️ P2SHAWdtCUuJmNjYuej2P6C7RA2SGtHscHZriH

Merkle Root

e4b202706fa31ef33aba043796bedd29964cc6268178cc5021fcc268ff450712

Transactions (1)

Coinbasee4b202706fa31e…fcc268ff450712

1 in → 1 out15.6800 XPM108 B

AWdtCUuJ…HscHZriH

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.

2.750 × 10⁹⁶(97-digit number)

27502130267736108019…92047183266818077559

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

2.750 × 10⁹⁶(97-digit number)

27502130267736108019…92047183266818077559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.750 × 10⁹⁶(97-digit number)

27502130267736108019…92047183266818077561

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

5.500 × 10⁹⁶(97-digit number)

55004260535472216038…84094366533636155119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.500 × 10⁹⁶(97-digit number)

55004260535472216038…84094366533636155121

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

1.100 × 10⁹⁷(98-digit number)

11000852107094443207…68188733067272310239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.100 × 10⁹⁷(98-digit number)

11000852107094443207…68188733067272310241

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

2.200 × 10⁹⁷(98-digit number)

22001704214188886415…36377466134544620479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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