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Block #2,100,705

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/5/2017, 9:25:45 AM · Difficulty 10.8557 · 4,738,722 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

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

4,738,722

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…33642191953435982240

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.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 2100705

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock d2c0d4281daf8bd6c3529b4a9dca6ca61b9fe999acb3e91aef67f4ad2ceff57d

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,100,705 on Chainz ↗

Block #2,100,705

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