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Home/Chain Registry/Block #195,968

Block #195,968

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/6/2013, 4:34:27 AM Β· Difficulty 9.8802 Β· 6,601,295 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
09e74a317ba7660a43078a93b80e0b484828eeabb4c1747a38271defcd06dc25
View on Chainz β†—

Height

#195,968

Difficulty

9.880187

Transactions

1

Size

206 B

Version

2

Bits

09e153ef

Nonce

1,592

Timestamp

10/6/2013, 4:34:27 AM

Confirmations

6,601,295

Merkle Root

7f391b6b4a607df39b14fa207fe6cde174682381d14eecc6d7c4571bdba64b22
Transactions (1)
Coinbase7f391b6b4a607d…c4571bdba64b22
1 in β†’ 1 out10.2300 XPM116 B
AcLBm5Z9…S683d7c3
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.

5.752 Γ— 10⁹³(94-digit number)
57521514140473082445…22731454069973767000
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
5.752 Γ— 10⁹³(94-digit number)
57521514140473082445…22731454069973767001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.150 Γ— 10⁹⁴(95-digit number)
11504302828094616489…45462908139947534001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.300 Γ— 10⁹⁴(95-digit number)
23008605656189232978…90925816279895068001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.601 Γ— 10⁹⁴(95-digit number)
46017211312378465956…81851632559790136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.203 Γ— 10⁹⁴(95-digit number)
92034422624756931912…63703265119580272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.840 Γ— 10⁹⁡(96-digit number)
18406884524951386382…27406530239160544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.681 Γ— 10⁹⁡(96-digit number)
36813769049902772764…54813060478321088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.362 Γ— 10⁹⁡(96-digit number)
73627538099805545529…09626120956642176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.472 Γ— 10⁹⁢(97-digit number)
14725507619961109105…19252241913284352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.945 Γ— 10⁹⁢(97-digit number)
29451015239922218211…38504483826568704001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
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 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 195968

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 09e74a317ba7660a43078a93b80e0b484828eeabb4c1747a38271defcd06dc25

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 #195,968 on Chainz β†—
Circulating Supply:57,622,132 XPMΒ·at block #6,797,262 Β· updates every 60s
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