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Block #435,856

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/9/2014, 5:32:04 AM Β· Difficulty 10.3537 Β· 6,359,768 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c55e9c8e769c095adf4fa0f739e20ac4e89fe8f39790deea5e6e02581b7cba50
View on Chainz β†—

Height

#435,856

Difficulty

10.353710

Transactions

1

Size

203 B

Version

2

Bits

0a5a8cc2

Nonce

140,965

Timestamp

3/9/2014, 5:32:04 AM

Confirmations

6,359,768

Merkle Root

fdbea96205472f39fc05bd0720c86e5b99888008984f5c9b2a1d14ed3486f90c
Transactions (1)
Coinbasefdbea96205472f…1d14ed3486f90c
1 in β†’ 1 out9.3100 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.286 Γ— 10¹⁰¹(102-digit number)
22863906808684239929…27677162629226216480
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
2.286 Γ— 10¹⁰¹(102-digit number)
22863906808684239929…27677162629226216479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.572 Γ— 10¹⁰¹(102-digit number)
45727813617368479858…55354325258452432959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.145 Γ— 10¹⁰¹(102-digit number)
91455627234736959716…10708650516904865919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.829 Γ— 10¹⁰²(103-digit number)
18291125446947391943…21417301033809731839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.658 Γ— 10¹⁰²(103-digit number)
36582250893894783886…42834602067619463679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.316 Γ— 10¹⁰²(103-digit number)
73164501787789567773…85669204135238927359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.463 Γ— 10¹⁰³(104-digit number)
14632900357557913554…71338408270477854719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.926 Γ— 10¹⁰³(104-digit number)
29265800715115827109…42676816540955709439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.853 Γ— 10¹⁰³(104-digit number)
58531601430231654218…85353633081911418879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.170 Γ— 10¹⁰⁴(105-digit number)
11706320286046330843…70707266163822837759
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 435856

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 c55e9c8e769c095adf4fa0f739e20ac4e89fe8f39790deea5e6e02581b7cba50

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 #435,856 on Chainz β†—
Circulating Supply:57,609,059 XPMΒ·at block #6,795,623 Β· updates every 60s
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