Block #27,046

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 7:27:25 AM · Difficulty 7.9775 · 6,767,198 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c36f84b3362dd8410241b4c8ed6f4cb5e0558df444e3f8e270a81acc40a840ce

View on Chainz ↗

Height

#27,046

Difficulty

7.977462

Transactions

Size

1.95 KB

Version

Bits

07fa3af3

Nonce

258

Timestamp

7/13/2013, 7:27:25 AM

Confirmations

6,767,198

Merkle Root

8eae2d40130539b7705b39816f2d3ddc227b275bff76a580da14f704b01395df

Transactions (3)

Coinbase1bc54bea374c19…e4f61a82940195

1 in → 1 out15.7200 XPM108 B

AcML4AoS…1weWdvab

882f5e32cae8ff…78aab011471c82

14 in → 1 out251.5400 XPM1.60 KB

AaNMrVuB…vz8xMmHF

e9aaccd77d0812…4917ea677663c3

1 in → 1 out15.7600 XPM159 B

AMTQYzw7…EjLeQYH7

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.

3.473 × 10⁹⁶(97-digit number)

34734023234000282388…45863231639206720969

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

3.473 × 10⁹⁶(97-digit number)

34734023234000282388…45863231639206720969

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.473 × 10⁹⁶(97-digit number)

34734023234000282388…45863231639206720971

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

6.946 × 10⁹⁶(97-digit number)

69468046468000564776…91726463278413441939

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.946 × 10⁹⁶(97-digit number)

69468046468000564776…91726463278413441941

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

1.389 × 10⁹⁷(98-digit number)

13893609293600112955…83452926556826883879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.389 × 10⁹⁷(98-digit number)

13893609293600112955…83452926556826883881

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

2.778 × 10⁹⁷(98-digit number)

27787218587200225910…66905853113653767759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.778 × 10⁹⁷(98-digit number)

27787218587200225910…66905853113653767761

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