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Home/Chain Registry/Block #1,850,278

Block #1,850,278

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/15/2016, 2:56:22 PM Β· Difficulty 10.6289 Β· 4,992,565 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
146fe942d63995578025bc39fbc44b2ff441ab9b9bb8b324ce129198ace16cb5
View on Chainz β†—

Difficulty

10.628920

Transactions

1

Size

199 B

Version

2

Bits

0aa100e8

Nonce

2,144,649,964

Timestamp

11/15/2016, 2:56:22 PM

Confirmations

4,992,565

Merkle Root

e3a7e4183222d02dfc0ddf634c36ff6a8ff97c86ea61d4606ea375d20d5f7374
Transactions (1)
Coinbasee3a7e4183222d0…a375d20d5f7374
1 in β†’ 1 out8.8400 XPM109 B
AdzgpVJc…zJrZXUBC
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.

8.124 Γ— 10⁹³(94-digit number)
81249350750603909394…07498877951116640000
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
8.124 Γ— 10⁹³(94-digit number)
81249350750603909394…07498877951116640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.624 Γ— 10⁹⁴(95-digit number)
16249870150120781878…14997755902233280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.249 Γ— 10⁹⁴(95-digit number)
32499740300241563757…29995511804466560001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.499 Γ— 10⁹⁴(95-digit number)
64999480600483127515…59991023608933120001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.299 Γ— 10⁹⁡(96-digit number)
12999896120096625503…19982047217866240001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.599 Γ— 10⁹⁡(96-digit number)
25999792240193251006…39964094435732480001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.199 Γ— 10⁹⁡(96-digit number)
51999584480386502012…79928188871464960001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.039 Γ— 10⁹⁢(97-digit number)
10399916896077300402…59856377742929920001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.079 Γ— 10⁹⁢(97-digit number)
20799833792154600805…19712755485859840001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.159 Γ— 10⁹⁢(97-digit number)
41599667584309201610…39425510971719680001
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 1850278

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 146fe942d63995578025bc39fbc44b2ff441ab9b9bb8b324ce129198ace16cb5

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 #1,850,278 on Chainz β†—
Circulating Supply:57,987,088 XPMΒ·at block #6,842,842 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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