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Block #288,760

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/1/2013, 9:53:41 PM Β· Difficulty 9.9879 Β· 6,511,904 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ca7215a8f4ce808f78d45b1bee82df13ad069d94095bfea2c547e35f17a43dba
View on Chainz β†—

Height

#288,760

Difficulty

9.987934

Transactions

1

Size

210 B

Version

2

Bits

09fce944

Nonce

32,390

Timestamp

12/1/2013, 9:53:41 PM

Confirmations

6,511,904

Merkle Root

ec69f78676fb85ab204b10dd8fd46e798331fc86e127a9d53a48d2bf50c63532
Transactions (1)
Coinbaseec69f78676fb85…48d2bf50c63532
1 in β†’ 1 out10.0100 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.317 Γ— 10¹⁰³(104-digit number)
13178200377103013325…48874952542348917760
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
1.317 Γ— 10¹⁰³(104-digit number)
13178200377103013325…48874952542348917759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.635 Γ— 10¹⁰³(104-digit number)
26356400754206026650…97749905084697835519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.271 Γ— 10¹⁰³(104-digit number)
52712801508412053300…95499810169395671039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.054 Γ— 10¹⁰⁴(105-digit number)
10542560301682410660…90999620338791342079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.108 Γ— 10¹⁰⁴(105-digit number)
21085120603364821320…81999240677582684159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.217 Γ— 10¹⁰⁴(105-digit number)
42170241206729642640…63998481355165368319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.434 Γ— 10¹⁰⁴(105-digit number)
84340482413459285280…27996962710330736639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.686 Γ— 10¹⁰⁡(106-digit number)
16868096482691857056…55993925420661473279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.373 Γ— 10¹⁰⁡(106-digit number)
33736192965383714112…11987850841322946559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.747 Γ— 10¹⁰⁡(106-digit number)
67472385930767428224…23975701682645893119
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 288760

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 ca7215a8f4ce808f78d45b1bee82df13ad069d94095bfea2c547e35f17a43dba

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 #288,760 on Chainz β†—
Circulating Supply:57,649,374 XPMΒ·at block #6,800,663 Β· updates every 60s
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