Block #1,110,990

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/16/2015, 7:40:32 PM · Difficulty 10.8790 · 5,703,105 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d4e324a4dde66b1f6d090878d5d3091ba3a78f1ca354dbc51d6f645098457305

View on Chainz ↗

Height

#1,110,990

Difficulty

10.879019

Transactions

Size

3.31 KB

Version

Bits

0ae10764

Nonce

225,623,435

Timestamp

6/16/2015, 7:40:32 PM

Confirmations

5,703,105

Mined by

⛏️ P2SHAHJKj23aCeo2RkQ4MCv81cKQFacZLfaZ6y

Merkle Root

88de5046cc180ded457cfb7728a8a8d2375acee159174c68802e83a036232336

Transactions (2)

Coinbasefb970913bb6daa…92fa015d4d3d01

1 in → 1 out8.4800 XPM110 B

AHJKj23a…cZLfaZ6y

588d503572e4d4…fbad177bb3e068

21 in → 2 out323.9566 XPM3.11 KB

AaTkPtLs…Vzvedt1n AQHE5e6H…xDwU3vYU

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.

3.451 × 10⁹⁸(99-digit number)

34515469598996387289…90685095370875863039

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

3.451 × 10⁹⁸(99-digit number)

34515469598996387289…90685095370875863039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.451 × 10⁹⁸(99-digit number)

34515469598996387289…90685095370875863041

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

6.903 × 10⁹⁸(99-digit number)

69030939197992774579…81370190741751726079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.903 × 10⁹⁸(99-digit number)

69030939197992774579…81370190741751726081

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

1.380 × 10⁹⁹(100-digit number)

13806187839598554915…62740381483503452159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.380 × 10⁹⁹(100-digit number)

13806187839598554915…62740381483503452161

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

2.761 × 10⁹⁹(100-digit number)

27612375679197109831…25480762967006904319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.761 × 10⁹⁹(100-digit number)

27612375679197109831…25480762967006904321

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

5.522 × 10⁹⁹(100-digit number)

55224751358394219663…50961525934013808639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.522 × 10⁹⁹(100-digit number)

55224751358394219663…50961525934013808641

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #1,110,990

Cookie Preferences