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Block #193,430

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/4/2013, 12:27:48 PM Β· Difficulty 9.8765 Β· 6,633,818 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b4bb1335bf406fe84b2dd17aa09f283d4577ffbdede5cf8c845cd7286c190356
View on Chainz β†—

Height

#193,430

Difficulty

9.876462

Transactions

1

Size

197 B

Version

2

Bits

09e05fd7

Nonce

558,697

Timestamp

10/4/2013, 12:27:48 PM

Confirmations

6,633,818

Merkle Root

60d8be33520cbebcd635626d8c5c5f695256cc4bf4bacb1f856c557e59fb5eef
Transactions (1)
Coinbase60d8be33520cbe…6c557e59fb5eef
1 in β†’ 1 out10.2400 XPM109 B
AXbpyooS…bup7bQTH
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.

2.780 Γ— 10⁹⁰(91-digit number)
27804973662171954434…37619829709432967400
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.780 Γ— 10⁹⁰(91-digit number)
27804973662171954434…37619829709432967399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.560 Γ— 10⁹⁰(91-digit number)
55609947324343908869…75239659418865934799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.112 Γ— 10⁹¹(92-digit number)
11121989464868781773…50479318837731869599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.224 Γ— 10⁹¹(92-digit number)
22243978929737563547…00958637675463739199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.448 Γ— 10⁹¹(92-digit number)
44487957859475127095…01917275350927478399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.897 Γ— 10⁹¹(92-digit number)
88975915718950254191…03834550701854956799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.779 Γ— 10⁹²(93-digit number)
17795183143790050838…07669101403709913599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.559 Γ— 10⁹²(93-digit number)
35590366287580101676…15338202807419827199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.118 Γ— 10⁹²(93-digit number)
71180732575160203353…30676405614839654399
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 193430

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 b4bb1335bf406fe84b2dd17aa09f283d4577ffbdede5cf8c845cd7286c190356

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 #193,430 on Chainz β†—
Circulating Supply:57,862,087 XPMΒ·at block #6,827,247 Β· updates every 60s
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