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Block #359,807

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/15/2014, 1:10:44 AM Β· Difficulty 10.3882 Β· 6,477,472 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9c1c9765c077f24b52239ad5df8504d406a7326c193ef213c1004f705c43a445
View on Chainz β†—

Height

#359,807

Difficulty

10.388152

Transactions

1

Size

204 B

Version

2

Bits

0a635df3

Nonce

53,141

Timestamp

1/15/2014, 1:10:44 AM

Confirmations

6,477,472

Merkle Root

7bdc016d2bdbc20cf878bbea85c61fb3d8a438deb9d423d54d100b012bc5908d
Transactions (1)
Coinbase7bdc016d2bdbc2…100b012bc5908d
1 in β†’ 1 out9.2500 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.

1.648 Γ— 10¹⁰⁡(106-digit number)
16481014120878780439…61975646713684823040
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
1.648 Γ— 10¹⁰⁡(106-digit number)
16481014120878780439…61975646713684823039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.296 Γ— 10¹⁰⁡(106-digit number)
32962028241757560879…23951293427369646079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.592 Γ— 10¹⁰⁡(106-digit number)
65924056483515121758…47902586854739292159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.318 Γ— 10¹⁰⁢(107-digit number)
13184811296703024351…95805173709478584319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.636 Γ— 10¹⁰⁢(107-digit number)
26369622593406048703…91610347418957168639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.273 Γ— 10¹⁰⁢(107-digit number)
52739245186812097407…83220694837914337279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.054 Γ— 10¹⁰⁷(108-digit number)
10547849037362419481…66441389675828674559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.109 Γ— 10¹⁰⁷(108-digit number)
21095698074724838962…32882779351657349119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.219 Γ— 10¹⁰⁷(108-digit number)
42191396149449677925…65765558703314698239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.438 Γ— 10¹⁰⁷(108-digit number)
84382792298899355851…31531117406629396479
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 359807

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 9c1c9765c077f24b52239ad5df8504d406a7326c193ef213c1004f705c43a445

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 #359,807 on Chainz β†—
Circulating Supply:57,942,544 XPMΒ·at block #6,837,278 Β· updates every 60s
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