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Block #352,260

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/10/2014, 5:43:47 AM Β· Difficulty 10.3048 Β· 6,455,869 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dbecc19eef9bf4dc7b88dbeb9bcca9d38d4e79b61b9f86f764990cb6cdaf66fa
View on Chainz β†—

Height

#352,260

Difficulty

10.304840

Transactions

1

Size

202 B

Version

2

Bits

0a4e0a03

Nonce

165,537

Timestamp

1/10/2014, 5:43:47 AM

Confirmations

6,455,869

Merkle Root

b8e373fd8861805e0f7023682806979c8d5519f798c3e633b90bb424d9f84e63
Transactions (1)
Coinbaseb8e373fd886180…0bb424d9f84e63
1 in β†’ 1 out9.4000 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.496 Γ— 10⁹⁸(99-digit number)
14960199753481858941…62452748202187515940
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
1.496 Γ— 10⁹⁸(99-digit number)
14960199753481858941…62452748202187515939
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.992 Γ— 10⁹⁸(99-digit number)
29920399506963717882…24905496404375031879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.984 Γ— 10⁹⁸(99-digit number)
59840799013927435764…49810992808750063759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.196 Γ— 10⁹⁹(100-digit number)
11968159802785487152…99621985617500127519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.393 Γ— 10⁹⁹(100-digit number)
23936319605570974305…99243971235000255039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.787 Γ— 10⁹⁹(100-digit number)
47872639211141948611…98487942470000510079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.574 Γ— 10⁹⁹(100-digit number)
95745278422283897222…96975884940001020159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.914 Γ— 10¹⁰⁰(101-digit number)
19149055684456779444…93951769880002040319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.829 Γ— 10¹⁰⁰(101-digit number)
38298111368913558888…87903539760004080639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.659 Γ— 10¹⁰⁰(101-digit number)
76596222737827117777…75807079520008161279
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 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
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 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 352260

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 dbecc19eef9bf4dc7b88dbeb9bcca9d38d4e79b61b9f86f764990cb6cdaf66fa

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 #352,260 on Chainz β†—
Circulating Supply:57,709,073 XPMΒ·at block #6,808,128 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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