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Block #205,758

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/12/2013, 8:42:23 AM Β· Difficulty 9.9004 Β· 6,621,016 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
47fc1e92eb117f24b5993bc34f8e7a0ed25f76ccc49ba30ea4e7ec61eda60850
View on Chainz β†—

Height

#205,758

Difficulty

9.900431

Transactions

1

Size

198 B

Version

2

Bits

09e682ab

Nonce

175,202

Timestamp

10/12/2013, 8:42:23 AM

Confirmations

6,621,016

Merkle Root

368de559cd3dc2875dfd93b598d3fe89e8150eb8e97c6d4cd670552563fd66e3
Transactions (1)
Coinbase368de559cd3dc2…70552563fd66e3
1 in β†’ 1 out10.1900 XPM109 B
AXJRKXUR…FLrnL43v
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.

7.315 Γ— 10⁹²(93-digit number)
73159407062519830101…79716998544271434500
Discovered Prime Numbers
p_k = 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.

1
origin + 1
7.315 Γ— 10⁹²(93-digit number)
73159407062519830101…79716998544271434501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.463 Γ— 10⁹³(94-digit number)
14631881412503966020…59433997088542869001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.926 Γ— 10⁹³(94-digit number)
29263762825007932040…18867994177085738001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.852 Γ— 10⁹³(94-digit number)
58527525650015864080…37735988354171476001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.170 Γ— 10⁹⁴(95-digit number)
11705505130003172816…75471976708342952001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.341 Γ— 10⁹⁴(95-digit number)
23411010260006345632…50943953416685904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.682 Γ— 10⁹⁴(95-digit number)
46822020520012691264…01887906833371808001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.364 Γ— 10⁹⁴(95-digit number)
93644041040025382529…03775813666743616001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.872 Γ— 10⁹⁡(96-digit number)
18728808208005076505…07551627333487232001
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 Cunningham Chain of the Second Kind. 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 205758

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 47fc1e92eb117f24b5993bc34f8e7a0ed25f76ccc49ba30ea4e7ec61eda60850

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 #205,758 on Chainz β†—
Circulating Supply:57,858,351 XPMΒ·at block #6,826,773 Β· updates every 60s
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