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Home/Chain Registry/Block #303,531

Block #303,531

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/10/2013, 10:33:46 AM Β· Difficulty 9.9930 Β· 6,492,855 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
28c7ae7762b8dcd20d7b98ba57357e15c83677d8a67a06db23c9b2289ebefa69
View on Chainz β†—

Height

#303,531

Difficulty

9.993037

Transactions

1

Size

207 B

Version

2

Bits

09fe37ac

Nonce

8,186

Timestamp

12/10/2013, 10:33:46 AM

Confirmations

6,492,855

Merkle Root

1e07119dc2e859495efb63abcdacc646261a63dedec4dfe269c69a421bbe45f9
Transactions (1)
Coinbase1e07119dc2e859…c69a421bbe45f9
1 in β†’ 1 out10.0000 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.

1.637 Γ— 10⁹⁸(99-digit number)
16375961205104590098…39023473156771379200
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
1.637 Γ— 10⁹⁸(99-digit number)
16375961205104590098…39023473156771379199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.275 Γ— 10⁹⁸(99-digit number)
32751922410209180196…78046946313542758399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.550 Γ— 10⁹⁸(99-digit number)
65503844820418360392…56093892627085516799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.310 Γ— 10⁹⁹(100-digit number)
13100768964083672078…12187785254171033599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.620 Γ— 10⁹⁹(100-digit number)
26201537928167344157…24375570508342067199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.240 Γ— 10⁹⁹(100-digit number)
52403075856334688314…48751141016684134399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.048 Γ— 10¹⁰⁰(101-digit number)
10480615171266937662…97502282033368268799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.096 Γ— 10¹⁰⁰(101-digit number)
20961230342533875325…95004564066736537599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.192 Γ— 10¹⁰⁰(101-digit number)
41922460685067750651…90009128133473075199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.384 Γ— 10¹⁰⁰(101-digit number)
83844921370135501302…80018256266946150399
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 303531

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 28c7ae7762b8dcd20d7b98ba57357e15c83677d8a67a06db23c9b2289ebefa69

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 #303,531 on Chainz β†—
Circulating Supply:57,615,085 XPMΒ·at block #6,796,385 Β· updates every 60s
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