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Block #2,635,329

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 5:20:01 AM Β· Difficulty 11.3070 Β· 4,196,482 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c17de634ac09f9f28d76bc3a68aca5594cb86045283f42da37140140e563ba20
View on Chainz β†—

Difficulty

11.307000

Transactions

1

Size

200 B

Version

2

Bits

0b4e978a

Nonce

111,020,820

Timestamp

4/29/2018, 5:20:01 AM

Confirmations

4,196,482

Merkle Root

8082e947aa7e5f545b731113d2d344b2791206d0a0dabb2bc67d79dee80dadfa
Transactions (1)
Coinbase8082e947aa7e5f…7d79dee80dadfa
1 in β†’ 1 out7.8100 XPM110 B
AS2BS8cf…RDdFpXW9
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.

6.429 Γ— 10⁹³(94-digit number)
64295794146834724644…98795812714255075820
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
6.429 Γ— 10⁹³(94-digit number)
64295794146834724644…98795812714255075821
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.285 Γ— 10⁹⁴(95-digit number)
12859158829366944928…97591625428510151641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.571 Γ— 10⁹⁴(95-digit number)
25718317658733889857…95183250857020303281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.143 Γ— 10⁹⁴(95-digit number)
51436635317467779715…90366501714040606561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.028 Γ— 10⁹⁡(96-digit number)
10287327063493555943…80733003428081213121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.057 Γ— 10⁹⁡(96-digit number)
20574654126987111886…61466006856162426241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.114 Γ— 10⁹⁡(96-digit number)
41149308253974223772…22932013712324852481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.229 Γ— 10⁹⁡(96-digit number)
82298616507948447544…45864027424649704961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.645 Γ— 10⁹⁢(97-digit number)
16459723301589689508…91728054849299409921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.291 Γ— 10⁹⁢(97-digit number)
32919446603179379017…83456109698598819841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.583 Γ— 10⁹⁢(97-digit number)
65838893206358758035…66912219397197639681
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 2635329

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 c17de634ac09f9f28d76bc3a68aca5594cb86045283f42da37140140e563ba20

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 #2,635,329 on Chainz β†—
Circulating Supply:57,898,603 XPMΒ·at block #6,831,810 Β· updates every 60s
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