Block #2,778,152

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 8/4/2018, 1:09:21 AM · Difficulty 11.6517 · 4,038,146 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb809ec43ecc148a1bb3413e924f54805f7268b6441f275bb187a1bff1d6233a

View on Chainz ↗

Height

#2,778,152

Difficulty

11.651717

Transactions

Size

813 B

Version

Bits

0ba6d6ef

Nonce

566,160,139

Timestamp

8/4/2018, 1:09:21 AM

Confirmations

4,038,146

Mined by

⛏️ P2SHAd1YgfgA7MuXzTCEDCmPXzVg367qGgTZsD

Merkle Root

c344df4d17646d865ffad7aa8b224b26a7b8694d77876cbacfeba27ae5d772a9

Transactions (3)

Coinbased821e11d7a6375…597bca2368d95b

1 in → 1 out7.3700 XPM110 B

Ad1YgfgA…7qGgTZsD

ea3361549b04d9…6150b34ada763a

2 in → 2 out14.6700 XPM305 B

AUAVwVPF…gha5UXKS ANiRSGwW…LtXULkMk

daa67a1858e128…efed9b0c5a8fc8

2 in → 2 out14.6700 XPM308 B

AZrrkiXx…HEKyFuAh ATC9arG9…SM9op26h

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.

6.792 × 10⁹⁴(95-digit number)

67926510434971323626…82161376763335516159

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

6.792 × 10⁹⁴(95-digit number)

67926510434971323626…82161376763335516159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.792 × 10⁹⁴(95-digit number)

67926510434971323626…82161376763335516161

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

1.358 × 10⁹⁵(96-digit number)

13585302086994264725…64322753526671032319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.358 × 10⁹⁵(96-digit number)

13585302086994264725…64322753526671032321

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

2.717 × 10⁹⁵(96-digit number)

27170604173988529450…28645507053342064639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.717 × 10⁹⁵(96-digit number)

27170604173988529450…28645507053342064641

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

5.434 × 10⁹⁵(96-digit number)

54341208347977058901…57291014106684129279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.434 × 10⁹⁵(96-digit number)

54341208347977058901…57291014106684129281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.086 × 10⁹⁶(97-digit number)

10868241669595411780…14582028213368258559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.086 × 10⁹⁶(97-digit number)

10868241669595411780…14582028213368258561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.173 × 10⁹⁶(97-digit number)

21736483339190823560…29164056426736517119

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

2.173 × 10⁹⁶(97-digit number)

21736483339190823560…29164056426736517121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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

Block #2,778,152

Cookie Preferences