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Home/Chain Registry/Block #1,436,161

Block #1,436,161

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/30/2016, 1:32:23 PM Β· Difficulty 10.8067 Β· 5,409,458 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
71979e233775d81bac4d966bff3a48eb73b0e10523764727817f03240939b2ae
View on Chainz β†—

Difficulty

10.806679

Transactions

2

Size

14.40 KB

Version

2

Bits

0ace827c

Nonce

167,169,202

Timestamp

1/30/2016, 1:32:23 PM

Confirmations

5,409,458

Merkle Root

988567e66dafbb6282099ea9b835b498a36a4e8b5c8c36d93e4ca385d1fb0982
Transactions (2)
Coinbaseabf3a3ccbb0f95…b288d62d0c1ce6
1 in β†’ 1 out8.7000 XPM110 B
AYW2kTno…1viHbDBY
9c3b25ffa2e665…1a59634647ffb3
98 in β†’ 1 out6.5623 XPM14.20 KB
AGjfN59n…XRyWCGwx
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.

3.353 Γ— 10⁹⁰(91-digit number)
33537740241623287026…97468859434700467880
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
3.353 Γ— 10⁹⁰(91-digit number)
33537740241623287026…97468859434700467879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.707 Γ— 10⁹⁰(91-digit number)
67075480483246574053…94937718869400935759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.341 Γ— 10⁹¹(92-digit number)
13415096096649314810…89875437738801871519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.683 Γ— 10⁹¹(92-digit number)
26830192193298629621…79750875477603743039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.366 Γ— 10⁹¹(92-digit number)
53660384386597259243…59501750955207486079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.073 Γ— 10⁹²(93-digit number)
10732076877319451848…19003501910414972159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.146 Γ— 10⁹²(93-digit number)
21464153754638903697…38007003820829944319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.292 Γ— 10⁹²(93-digit number)
42928307509277807394…76014007641659888639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.585 Γ— 10⁹²(93-digit number)
85856615018555614788…52028015283319777279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.717 Γ— 10⁹³(94-digit number)
17171323003711122957…04056030566639554559
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 1436161

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 71979e233775d81bac4d966bff3a48eb73b0e10523764727817f03240939b2ae

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 #1,436,161 on Chainz β†—
Circulating Supply:58,009,399 XPMΒ·at block #6,845,618 Β· updates every 60s
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