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Block #237,180

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/31/2013, 9:38:16 PM Β· Difficulty 9.9493 Β· 6,560,103 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e24b6a0cde4f014445fb4192b8e6a3086db5dc22b886679c34d2a43f9d50aa58
View on Chainz β†—

Height

#237,180

Difficulty

9.949317

Transactions

1

Size

210 B

Version

2

Bits

09f30675

Nonce

67,110,035

Timestamp

10/31/2013, 9:38:16 PM

Confirmations

6,560,103

Merkle Root

7da484c1032a07f0b30ccb86108284d0ed640966fe0d61561c0bb49a76d96aa3
Transactions (1)
Coinbase7da484c1032a07…0bb49a76d96aa3
1 in β†’ 1 out10.0900 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.

8.304 Γ— 10¹⁰⁴(105-digit number)
83045289773470420522…83517955180084879680
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
8.304 Γ— 10¹⁰⁴(105-digit number)
83045289773470420522…83517955180084879679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.660 Γ— 10¹⁰⁡(106-digit number)
16609057954694084104…67035910360169759359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.321 Γ— 10¹⁰⁡(106-digit number)
33218115909388168209…34071820720339518719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.643 Γ— 10¹⁰⁡(106-digit number)
66436231818776336418…68143641440679037439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.328 Γ— 10¹⁰⁢(107-digit number)
13287246363755267283…36287282881358074879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.657 Γ— 10¹⁰⁢(107-digit number)
26574492727510534567…72574565762716149759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.314 Γ— 10¹⁰⁢(107-digit number)
53148985455021069134…45149131525432299519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.062 Γ— 10¹⁰⁷(108-digit number)
10629797091004213826…90298263050864599039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.125 Γ— 10¹⁰⁷(108-digit number)
21259594182008427653…80596526101729198079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.251 Γ— 10¹⁰⁷(108-digit number)
42519188364016855307…61193052203458396159
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 237180

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 e24b6a0cde4f014445fb4192b8e6a3086db5dc22b886679c34d2a43f9d50aa58

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 #237,180 on Chainz β†—
Circulating Supply:57,622,293 XPMΒ·at block #6,797,282 Β· updates every 60s
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