Block #2,100,705

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/5/2017, 9:25:45 AM · Difficulty 10.8557 · 4,736,208 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2c0d4281daf8bd6c3529b4a9dca6ca61b9fe999acb3e91aef67f4ad2ceff57d

View on Chainz ↗

Height

#2,100,705

Difficulty

10.855690

Transactions

Size

426 B

Version

Bits

0adb0e85

Nonce

1,673,182,307

Timestamp

5/5/2017, 9:25:45 AM

Confirmations

4,736,208

Mined by

⛏️ P2SHAQ35J2MvkmcSTtkZrmQ7Jsh9vvJAZj7guY

Merkle Root

d25a72da0d5b337701ea47884c6761ee43555776fbd0f895b92e59ea5edbf84c

Transactions (2)

Coinbase04b1d6be246c0e…f070ac2273c610

1 in → 1 out8.4800 XPM110 B

AQ35J2Mv…JAZj7guY

177bdc58bb5a06…587fc738646544

1 in → 2 out48333.0323 XPM226 B

APMTspTX…fWNRSany AUSwiVZX…3EBbkJTx

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.

2.261 × 10⁹⁵(96-digit number)

22619613861489458381…33642191953435982239

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

2.261 × 10⁹⁵(96-digit number)

22619613861489458381…33642191953435982239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.261 × 10⁹⁵(96-digit number)

22619613861489458381…33642191953435982241

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

4.523 × 10⁹⁵(96-digit number)

45239227722978916762…67284383906871964479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.523 × 10⁹⁵(96-digit number)

45239227722978916762…67284383906871964481

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

9.047 × 10⁹⁵(96-digit number)

90478455445957833524…34568767813743928959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.047 × 10⁹⁵(96-digit number)

90478455445957833524…34568767813743928961

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

1.809 × 10⁹⁶(97-digit number)

18095691089191566704…69137535627487857919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.809 × 10⁹⁶(97-digit number)

18095691089191566704…69137535627487857921

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

3.619 × 10⁹⁶(97-digit number)

36191382178383133409…38275071254975715839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.619 × 10⁹⁶(97-digit number)

36191382178383133409…38275071254975715841

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 #2,100,705

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