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Block #309,360

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/13/2013, 1:49:15 PM Β· Difficulty 9.9948 Β· 6,489,293 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
557c7efc0f2dff1beaf5cdcd451c42c7666718103c6e0a71cec74d635e7d51b2
View on Chainz β†—

Height

#309,360

Difficulty

9.994799

Transactions

1

Size

209 B

Version

2

Bits

09feab2b

Nonce

8,724

Timestamp

12/13/2013, 1:49:15 PM

Confirmations

6,489,293

Merkle Root

95568d0b3607a11af7587f86cf8aea77094f19b08652d90a6227f6e8cc2a5551
Transactions (1)
Coinbase95568d0b3607a1…27f6e8cc2a5551
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.

3.480 Γ— 10¹⁰²(103-digit number)
34802705277739314591…84542533813639577600
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
3.480 Γ— 10¹⁰²(103-digit number)
34802705277739314591…84542533813639577599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.960 Γ— 10¹⁰²(103-digit number)
69605410555478629182…69085067627279155199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.392 Γ— 10¹⁰³(104-digit number)
13921082111095725836…38170135254558310399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.784 Γ— 10¹⁰³(104-digit number)
27842164222191451673…76340270509116620799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.568 Γ— 10¹⁰³(104-digit number)
55684328444382903346…52680541018233241599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.113 Γ— 10¹⁰⁴(105-digit number)
11136865688876580669…05361082036466483199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.227 Γ— 10¹⁰⁴(105-digit number)
22273731377753161338…10722164072932966399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.454 Γ— 10¹⁰⁴(105-digit number)
44547462755506322676…21444328145865932799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.909 Γ— 10¹⁰⁴(105-digit number)
89094925511012645353…42888656291731865599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.781 Γ— 10¹⁰⁡(106-digit number)
17818985102202529070…85777312583463731199
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 309360

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 557c7efc0f2dff1beaf5cdcd451c42c7666718103c6e0a71cec74d635e7d51b2

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 #309,360 on Chainz β†—
Circulating Supply:57,633,248 XPMΒ·at block #6,798,652 Β· updates every 60s
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