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Block #505,362

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/22/2014, 9:44:34 AM Β· Difficulty 10.8107 Β· 6,321,494 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e05116a011d6d1441655618851c1476100fc3847462e176166e4d0dbeb2e110b
View on Chainz β†—

Height

#505,362

Difficulty

10.810710

Transactions

1

Size

207 B

Version

2

Bits

0acf8aaf

Nonce

55,428

Timestamp

4/22/2014, 9:44:34 AM

Confirmations

6,321,494

Merkle Root

fbc8281e4c3a9cb14915fdb0939d1ecd6976734ea5ab5c2485a2bb16ce0491be
Transactions (1)
Coinbasefbc8281e4c3a9c…a2bb16ce0491be
1 in β†’ 1 out8.5400 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.

5.317 Γ— 10⁹⁷(98-digit number)
53174186444373112227…09967407242306878920
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
5.317 Γ— 10⁹⁷(98-digit number)
53174186444373112227…09967407242306878919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.063 Γ— 10⁹⁸(99-digit number)
10634837288874622445…19934814484613757839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.126 Γ— 10⁹⁸(99-digit number)
21269674577749244891…39869628969227515679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.253 Γ— 10⁹⁸(99-digit number)
42539349155498489782…79739257938455031359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.507 Γ— 10⁹⁸(99-digit number)
85078698310996979564…59478515876910062719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.701 Γ— 10⁹⁹(100-digit number)
17015739662199395912…18957031753820125439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.403 Γ— 10⁹⁹(100-digit number)
34031479324398791825…37914063507640250879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.806 Γ— 10⁹⁹(100-digit number)
68062958648797583651…75828127015280501759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.361 Γ— 10¹⁰⁰(101-digit number)
13612591729759516730…51656254030561003519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.722 Γ— 10¹⁰⁰(101-digit number)
27225183459519033460…03312508061122007039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.445 Γ— 10¹⁰⁰(101-digit number)
54450366919038066921…06625016122244014079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 505362

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 e05116a011d6d1441655618851c1476100fc3847462e176166e4d0dbeb2e110b

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 #505,362 on Chainz β†—
Circulating Supply:57,859,016 XPMΒ·at block #6,826,855 Β· updates every 60s
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