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Home/Chain Registry/Block #435,733

Block #435,733

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/9/2014, 3:36:23 AM Β· Difficulty 10.3525 Β· 6,366,133 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
32830702adb30e70a99758a9fb78690d8fa4b46beff8c980a6f37f2b87ad7113
View on Chainz β†—

Height

#435,733

Difficulty

10.352527

Transactions

1

Size

202 B

Version

2

Bits

0a5a3f38

Nonce

85,745

Timestamp

3/9/2014, 3:36:23 AM

Confirmations

6,366,133

Merkle Root

39f4915914557f259fcd500f6e9fd9d1775e710119266974da6d4c8c49de4ada
Transactions (1)
Coinbase39f4915914557f…6d4c8c49de4ada
1 in β†’ 1 out9.3200 XPM111 B
AeKSSsKF…bLCESScQ
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.

2.083 Γ— 10⁹⁢(97-digit number)
20837390441888195733…17487000170858256000
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
2.083 Γ— 10⁹⁢(97-digit number)
20837390441888195733…17487000170858255999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.167 Γ— 10⁹⁢(97-digit number)
41674780883776391466…34974000341716511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.334 Γ— 10⁹⁢(97-digit number)
83349561767552782933…69948000683433023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.666 Γ— 10⁹⁷(98-digit number)
16669912353510556586…39896001366866047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.333 Γ— 10⁹⁷(98-digit number)
33339824707021113173…79792002733732095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.667 Γ— 10⁹⁷(98-digit number)
66679649414042226346…59584005467464191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.333 Γ— 10⁹⁸(99-digit number)
13335929882808445269…19168010934928383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.667 Γ— 10⁹⁸(99-digit number)
26671859765616890538…38336021869856767999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.334 Γ— 10⁹⁸(99-digit number)
53343719531233781077…76672043739713535999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.066 Γ— 10⁹⁹(100-digit number)
10668743906246756215…53344087479427071999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.133 Γ— 10⁹⁹(100-digit number)
21337487812493512430…06688174958854143999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 435733

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 32830702adb30e70a99758a9fb78690d8fa4b46beff8c980a6f37f2b87ad7113

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 #435,733 on Chainz β†—
Circulating Supply:57,659,020 XPMΒ·at block #6,801,865 Β· updates every 60s
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