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Home/Chain Registry/Block #1,409,485

Block #1,409,485

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/12/2016, 12:45:12 AM Β· Difficulty 10.8062 Β· 5,417,054 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e89e9e54ed9e34e1e42401d3ae9a9db8d554cfe7e92bf7d1bee269cd011e6090
View on Chainz β†—

Difficulty

10.806208

Transactions

1

Size

201 B

Version

2

Bits

0ace63a6

Nonce

1,742,568,384

Timestamp

1/12/2016, 12:45:12 AM

Confirmations

5,417,054

Merkle Root

7708c5fdc362cde23ec2debdb631464caee2a1ecd7d7b838326081a3b93bb2a8
Transactions (1)
Coinbase7708c5fdc362cd…6081a3b93bb2a8
1 in β†’ 1 out8.5500 XPM110 B
AZH4k5eH…9oi7iQon
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.

2.046 Γ— 10⁹⁢(97-digit number)
20466550196765268475…55809879285777964800
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
2.046 Γ— 10⁹⁢(97-digit number)
20466550196765268475…55809879285777964799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.093 Γ— 10⁹⁢(97-digit number)
40933100393530536951…11619758571555929599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.186 Γ— 10⁹⁢(97-digit number)
81866200787061073903…23239517143111859199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.637 Γ— 10⁹⁷(98-digit number)
16373240157412214780…46479034286223718399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.274 Γ— 10⁹⁷(98-digit number)
32746480314824429561…92958068572447436799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.549 Γ— 10⁹⁷(98-digit number)
65492960629648859122…85916137144894873599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.309 Γ— 10⁹⁸(99-digit number)
13098592125929771824…71832274289789747199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.619 Γ— 10⁹⁸(99-digit number)
26197184251859543649…43664548579579494399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.239 Γ— 10⁹⁸(99-digit number)
52394368503719087298…87329097159158988799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.047 Γ— 10⁹⁹(100-digit number)
10478873700743817459…74658194318317977599
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 1409485

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 e89e9e54ed9e34e1e42401d3ae9a9db8d554cfe7e92bf7d1bee269cd011e6090

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 #1,409,485 on Chainz β†—
Circulating Supply:57,856,460 XPMΒ·at block #6,826,538 Β· updates every 60s
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