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Block #358,355

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/14/2014, 12:56:09 AM Β· Difficulty 10.3878 Β· 6,442,478 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7d697e743fad8d98ecbbe5f98f950bd28a4a4c47e9d5c64a27e1d3d65efdced4
View on Chainz β†—

Height

#358,355

Difficulty

10.387817

Transactions

1

Size

205 B

Version

2

Bits

0a6347f3

Nonce

15,562

Timestamp

1/14/2014, 12:56:09 AM

Confirmations

6,442,478

Merkle Root

4475cfa7b69aa8e2ccf79ce5c0c7739530076ef54b61116baaeda08b39a61a44
Transactions (1)
Coinbase4475cfa7b69aa8…eda08b39a61a44
1 in β†’ 1 out9.2500 XPM116 B
AbwWkWZt…kawDhufa
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.

1.116 Γ— 10⁹³(94-digit number)
11162519910326522450…40209991731204392600
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
1.116 Γ— 10⁹³(94-digit number)
11162519910326522450…40209991731204392599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.232 Γ— 10⁹³(94-digit number)
22325039820653044900…80419983462408785199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.465 Γ— 10⁹³(94-digit number)
44650079641306089801…60839966924817570399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.930 Γ— 10⁹³(94-digit number)
89300159282612179602…21679933849635140799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.786 Γ— 10⁹⁴(95-digit number)
17860031856522435920…43359867699270281599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.572 Γ— 10⁹⁴(95-digit number)
35720063713044871841…86719735398540563199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.144 Γ— 10⁹⁴(95-digit number)
71440127426089743682…73439470797081126399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.428 Γ— 10⁹⁡(96-digit number)
14288025485217948736…46878941594162252799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.857 Γ— 10⁹⁡(96-digit number)
28576050970435897472…93757883188324505599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.715 Γ— 10⁹⁡(96-digit number)
57152101940871794945…87515766376649011199
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 358355

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 7d697e743fad8d98ecbbe5f98f950bd28a4a4c47e9d5c64a27e1d3d65efdced4

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 #358,355 on Chainz β†—
Circulating Supply:57,650,722 XPMΒ·at block #6,800,832 Β· updates every 60s
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