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Block #503,525

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/21/2014, 3:48:57 AM Β· Difficulty 10.8088 Β· 6,337,297 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
36d32b70502d921e428b7204d743778d98f387b041106376e2de29c6773fda17
View on Chainz β†—

Height

#503,525

Difficulty

10.808844

Transactions

1

Size

207 B

Version

2

Bits

0acf106a

Nonce

439,175,996

Timestamp

4/21/2014, 3:48:57 AM

Confirmations

6,337,297

Merkle Root

8697c79bbbd89139f6350e5b86793162f5a1aaacb34ebd7af5a7d1db0caa618b
Transactions (1)
Coinbase8697c79bbbd891…a7d1db0caa618b
1 in β†’ 1 out8.5500 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.

7.119 Γ— 10⁹⁷(98-digit number)
71192793096468969562…86985474979149513200
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
7.119 Γ— 10⁹⁷(98-digit number)
71192793096468969562…86985474979149513199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.423 Γ— 10⁹⁸(99-digit number)
14238558619293793912…73970949958299026399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.847 Γ— 10⁹⁸(99-digit number)
28477117238587587824…47941899916598052799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.695 Γ— 10⁹⁸(99-digit number)
56954234477175175649…95883799833196105599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.139 Γ— 10⁹⁹(100-digit number)
11390846895435035129…91767599666392211199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.278 Γ— 10⁹⁹(100-digit number)
22781693790870070259…83535199332784422399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.556 Γ— 10⁹⁹(100-digit number)
45563387581740140519…67070398665568844799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.112 Γ— 10⁹⁹(100-digit number)
91126775163480281039…34140797331137689599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.822 Γ— 10¹⁰⁰(101-digit number)
18225355032696056207…68281594662275379199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.645 Γ— 10¹⁰⁰(101-digit number)
36450710065392112415…36563189324550758399
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 503525

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 36d32b70502d921e428b7204d743778d98f387b041106376e2de29c6773fda17

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 #503,525 on Chainz β†—
Circulating Supply:57,970,929 XPMΒ·at block #6,840,821 Β· updates every 60s
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