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Home/Chain Registry/Block #1,436,162

Block #1,436,162

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/30/2016, 1:32:37 PM Β· Difficulty 10.8066 Β· 5,408,896 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7799e4f8472ccf8b8b740ef9b3bf781d77bc120c122525f7cd7093b7640ec91e
View on Chainz β†—

Difficulty

10.806587

Transactions

1

Size

200 B

Version

2

Bits

0ace7c7f

Nonce

1,126,664,545

Timestamp

1/30/2016, 1:32:37 PM

Confirmations

5,408,896

Merkle Root

dfe77b09e8bd876a69f516e0e6387fd63c1a926ead95880766eceaea78a80b27
Transactions (1)
Coinbasedfe77b09e8bd87…eceaea78a80b27
1 in β†’ 1 out8.5500 XPM110 B
AeLXE86u…HJFRTHgB
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.

3.244 Γ— 10⁹³(94-digit number)
32444804075495842814…15741303457033989590
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
3.244 Γ— 10⁹³(94-digit number)
32444804075495842814…15741303457033989591
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.488 Γ— 10⁹³(94-digit number)
64889608150991685629…31482606914067979181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.297 Γ— 10⁹⁴(95-digit number)
12977921630198337125…62965213828135958361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.595 Γ— 10⁹⁴(95-digit number)
25955843260396674251…25930427656271916721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.191 Γ— 10⁹⁴(95-digit number)
51911686520793348503…51860855312543833441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.038 Γ— 10⁹⁡(96-digit number)
10382337304158669700…03721710625087666881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.076 Γ— 10⁹⁡(96-digit number)
20764674608317339401…07443421250175333761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.152 Γ— 10⁹⁡(96-digit number)
41529349216634678803…14886842500350667521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.305 Γ— 10⁹⁡(96-digit number)
83058698433269357606…29773685000701335041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.661 Γ— 10⁹⁢(97-digit number)
16611739686653871521…59547370001402670081
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 1436162

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 7799e4f8472ccf8b8b740ef9b3bf781d77bc120c122525f7cd7093b7640ec91e

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 #1,436,162 on Chainz β†—
Circulating Supply:58,004,889 XPMΒ·at block #6,845,057 Β· updates every 60s
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