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Block #212,170

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/16/2013, 3:18:22 AM Β· Difficulty 9.9183 Β· 6,588,041 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b23db87c0ec5d13b2cce0c84778c1a570e120294a293f2fdaf46c06b2a235c78
View on Chainz β†—

Height

#212,170

Difficulty

9.918311

Transactions

1

Size

199 B

Version

2

Bits

09eb166f

Nonce

173,313

Timestamp

10/16/2013, 3:18:22 AM

Confirmations

6,588,041

Merkle Root

ff0f1d43ed158d63d6178fffd2fc125bca7425ccde63f86c38aa4feed867cfd9
Transactions (1)
Coinbaseff0f1d43ed158d…aa4feed867cfd9
1 in β†’ 1 out10.1500 XPM110 B
AbuU1HhS…JPwsJEbB
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.063 Γ— 10⁹²(93-digit number)
60631450860790478742…63774435345816262320
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
6.063 Γ— 10⁹²(93-digit number)
60631450860790478742…63774435345816262319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.063 Γ— 10⁹²(93-digit number)
60631450860790478742…63774435345816262321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.212 Γ— 10⁹³(94-digit number)
12126290172158095748…27548870691632524639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.212 Γ— 10⁹³(94-digit number)
12126290172158095748…27548870691632524641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.425 Γ— 10⁹³(94-digit number)
24252580344316191496…55097741383265049279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.425 Γ— 10⁹³(94-digit number)
24252580344316191496…55097741383265049281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.850 Γ— 10⁹³(94-digit number)
48505160688632382993…10195482766530098559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.850 Γ— 10⁹³(94-digit number)
48505160688632382993…10195482766530098561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
9.701 Γ— 10⁹³(94-digit number)
97010321377264765987…20390965533060197119
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” 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 β†’
β˜…β˜†β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 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 212170

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 b23db87c0ec5d13b2cce0c84778c1a570e120294a293f2fdaf46c06b2a235c78

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 β†’ Debug Window β†’ 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 #212,170 on Chainz β†—
Circulating Supply:57,645,757 XPMΒ·at block #6,800,210 Β· updates every 60s
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