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Home/Chain Registry/Block #2,660,467

Block #2,660,467

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/14/2018, 10:38:47 AM Β· Difficulty 11.6351 Β· 4,181,872 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bd42759ea235f6976bf9b999e13d08e922a9188d29adb6bef96d10202fe80deb
View on Chainz β†—

Difficulty

11.635148

Transactions

2

Size

1018 B

Version

2

Bits

0ba2990e

Nonce

1,805,208,526

Timestamp

5/14/2018, 10:38:47 AM

Confirmations

4,181,872

Merkle Root

8990e807c58d69446819aa80b3c8f8ce5e811fe32eb409c88eb8dbbf77306c29
Transactions (2)
Coinbasebef6d72ee97c30…05c92dfb7b4750
1 in β†’ 1 out7.3800 XPM110 B
Aao964pW…escxHUu2
d7d006964ad951…325b2ce2337f49
5 in β†’ 2 out1355.3761 XPM818 B
ATSMDgh4…s7fPdnWSAXbkjKtU…bbu2XDF6
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.

1.653 Γ— 10⁹⁡(96-digit number)
16538001608910729393…93860172420129857720
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
1.653 Γ— 10⁹⁡(96-digit number)
16538001608910729393…93860172420129857719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.307 Γ— 10⁹⁡(96-digit number)
33076003217821458786…87720344840259715439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.615 Γ— 10⁹⁡(96-digit number)
66152006435642917572…75440689680519430879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.323 Γ— 10⁹⁢(97-digit number)
13230401287128583514…50881379361038861759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.646 Γ— 10⁹⁢(97-digit number)
26460802574257167029…01762758722077723519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.292 Γ— 10⁹⁢(97-digit number)
52921605148514334058…03525517444155447039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.058 Γ— 10⁹⁷(98-digit number)
10584321029702866811…07051034888310894079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.116 Γ— 10⁹⁷(98-digit number)
21168642059405733623…14102069776621788159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.233 Γ— 10⁹⁷(98-digit number)
42337284118811467246…28204139553243576319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.467 Γ— 10⁹⁷(98-digit number)
84674568237622934493…56408279106487152639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.693 Γ— 10⁹⁸(99-digit number)
16934913647524586898…12816558212974305279
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 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
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 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 2660467

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 bd42759ea235f6976bf9b999e13d08e922a9188d29adb6bef96d10202fe80deb

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 #2,660,467 on Chainz β†—
Circulating Supply:57,983,119 XPMΒ·at block #6,842,338 Β· updates every 60s
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