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Home/Chain Registry/Block #2,636,129

Block #2,636,129

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 11:28:05 AM Β· Difficulty 11.3640 Β· 4,195,659 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
540b005967229d3986640ca49df1ec9a0794eccacacaa2f1e301529b1582b85a
View on Chainz β†—

Difficulty

11.363954

Transactions

1

Size

200 B

Version

2

Bits

0b5d2c13

Nonce

1,318,075,557

Timestamp

4/29/2018, 11:28:05 AM

Confirmations

4,195,659

Merkle Root

65b8ae52895f8dcc2366430b9b170dc1666bdcf424d5da46ada8be9b37f45510
Transactions (1)
Coinbase65b8ae52895f8d…a8be9b37f45510
1 in β†’ 1 out7.7300 XPM110 B
AdXm2ZbE…jbaH3xq3
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.

6.172 Γ— 10⁹⁡(96-digit number)
61720590555459750416…12279854172281514240
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
6.172 Γ— 10⁹⁡(96-digit number)
61720590555459750416…12279854172281514241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.234 Γ— 10⁹⁢(97-digit number)
12344118111091950083…24559708344563028481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.468 Γ— 10⁹⁢(97-digit number)
24688236222183900166…49119416689126056961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.937 Γ— 10⁹⁢(97-digit number)
49376472444367800333…98238833378252113921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.875 Γ— 10⁹⁢(97-digit number)
98752944888735600666…96477666756504227841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.975 Γ— 10⁹⁷(98-digit number)
19750588977747120133…92955333513008455681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.950 Γ— 10⁹⁷(98-digit number)
39501177955494240266…85910667026016911361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.900 Γ— 10⁹⁷(98-digit number)
79002355910988480533…71821334052033822721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.580 Γ— 10⁹⁸(99-digit number)
15800471182197696106…43642668104067645441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.160 Γ— 10⁹⁸(99-digit number)
31600942364395392213…87285336208135290881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.320 Γ— 10⁹⁸(99-digit number)
63201884728790784426…74570672416270581761
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 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
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 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 2636129

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 540b005967229d3986640ca49df1ec9a0794eccacacaa2f1e301529b1582b85a

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 #2,636,129 on Chainz β†—
Circulating Supply:57,898,418 XPMΒ·at block #6,831,787 Β· updates every 60s
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