Home/Chain Registry/Block #212,860

Block #212,860

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/16/2013, 1:32:55 PM · Difficulty 9.9196 · 6,587,790 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b55aa0033443084c19bc89e1be3e1be5d898c4ef5c64ba5c579c89c29611ec65

View on Chainz ↗

Height

#212,860

Difficulty

9.919558

Transactions

Size

5.08 KB

Version

Bits

09eb6822

Nonce

1,164,788,324

Timestamp

10/16/2013, 1:32:55 PM

Confirmations

6,587,790

Merkle Root

76ef38c731a8bb9948c4e545b92aedb44dddad516f11b4a1a693dde281f248e3

Transactions (2)

Coinbaseeb942d718c8e60…fcaaf93449fa18

1 in → 143 out10.1000 XPM4.81 KB

AVe2Xy3t…SW5nzV7A AGbRhLj1…nZcEQFqQ Aa7VEgkw…Q8FyCCW3 ALSiuDiS…WqQxGQSY AaTyJe1r…9i8w83xa

1355c9f2e5884e…ee066bd17288ea

1 in → 2 out10.1700 XPM193 B

AQweB7Et…ZihHuQnP AQAvQSWZ…C9mFkvux

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.

5.208 × 10⁹⁹(100-digit number)

52087340726627396063…94128634881497369600

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

5.208 × 10⁹⁹(100-digit number)

52087340726627396063…94128634881497369599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.208 × 10⁹⁹(100-digit number)

52087340726627396063…94128634881497369601

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

1.041 × 10¹⁰⁰(101-digit number)

10417468145325479212…88257269762994739199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.041 × 10¹⁰⁰(101-digit number)

10417468145325479212…88257269762994739201

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

2.083 × 10¹⁰⁰(101-digit number)

20834936290650958425…76514539525989478399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.083 × 10¹⁰⁰(101-digit number)

20834936290650958425…76514539525989478401

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

4.166 × 10¹⁰⁰(101-digit number)

41669872581301916851…53029079051978956799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.166 × 10¹⁰⁰(101-digit number)

41669872581301916851…53029079051978956801

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

8.333 × 10¹⁰⁰(101-digit number)

83339745162603833702…06058158103957913599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 212860

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 b55aa0033443084c19bc89e1be3e1be5d898c4ef5c64ba5c579c89c29611ec65

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 #212,860 on Chainz ↗