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Block #420,168

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/26/2014, 5:18:20 AM Β· Difficulty 10.3670 Β· 6,406,759 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0fd1976db87b44b5fa7338cf407a7fe9fa9ce4f8a1fd93307a77ad7659f61e0f
View on Chainz β†—

Height

#420,168

Difficulty

10.366989

Transactions

1

Size

203 B

Version

2

Bits

0a5df302

Nonce

30,646

Timestamp

2/26/2014, 5:18:20 AM

Confirmations

6,406,759

Merkle Root

f1bebd056a022430abce1a3b8ae3eb5d95ae893f242dc67098f7bc417ca23082
Transactions (1)
Coinbasef1bebd056a0224…f7bc417ca23082
1 in β†’ 1 out9.2900 XPM111 B
AKmsgKwK…FS8PyNgv
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.

1.169 Γ— 10¹⁰⁰(101-digit number)
11691604957451542478…10728845675779801600
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
1.169 Γ— 10¹⁰⁰(101-digit number)
11691604957451542478…10728845675779801599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.338 Γ— 10¹⁰⁰(101-digit number)
23383209914903084956…21457691351559603199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.676 Γ— 10¹⁰⁰(101-digit number)
46766419829806169913…42915382703119206399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.353 Γ— 10¹⁰⁰(101-digit number)
93532839659612339826…85830765406238412799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.870 Γ— 10¹⁰¹(102-digit number)
18706567931922467965…71661530812476825599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.741 Γ— 10¹⁰¹(102-digit number)
37413135863844935930…43323061624953651199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.482 Γ— 10¹⁰¹(102-digit number)
74826271727689871861…86646123249907302399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.496 Γ— 10¹⁰²(103-digit number)
14965254345537974372…73292246499814604799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.993 Γ— 10¹⁰²(103-digit number)
29930508691075948744…46584492999629209599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.986 Γ— 10¹⁰²(103-digit number)
59861017382151897489…93168985999258419199
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 420168

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 0fd1976db87b44b5fa7338cf407a7fe9fa9ce4f8a1fd93307a77ad7659f61e0f

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 #420,168 on Chainz β†—
Circulating Supply:57,859,587 XPMΒ·at block #6,826,926 Β· updates every 60s
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