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Home/Chain Registry/Block #2,833,150

Block #2,833,150

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2018, 1:28:54 PM Β· Difficulty 11.7148 Β· 4,009,715 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6cdf6ffa29109bdb303c4afb302cd2cd161a694a590b219c9ae1ea592a2815d4
View on Chainz β†—

Difficulty

11.714818

Transactions

1

Size

199 B

Version

2

Bits

0bb6fe54

Nonce

1,370,922,460

Timestamp

9/10/2018, 1:28:54 PM

Confirmations

4,009,715

Merkle Root

90b7878f188e3379cfb0fcefc87ccc10cd8e9629a4f709e92e5848f976138850
Transactions (1)
Coinbase90b7878f188e33…5848f976138850
1 in β†’ 1 out7.2700 XPM110 B
AbFVYPmy…57GkGurN
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.

1.650 Γ— 10⁹³(94-digit number)
16500474999010525961…57152200671375941120
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
1.650 Γ— 10⁹³(94-digit number)
16500474999010525961…57152200671375941121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.300 Γ— 10⁹³(94-digit number)
33000949998021051922…14304401342751882241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.600 Γ— 10⁹³(94-digit number)
66001899996042103844…28608802685503764481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.320 Γ— 10⁹⁴(95-digit number)
13200379999208420768…57217605371007528961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.640 Γ— 10⁹⁴(95-digit number)
26400759998416841537…14435210742015057921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.280 Γ— 10⁹⁴(95-digit number)
52801519996833683075…28870421484030115841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.056 Γ— 10⁹⁡(96-digit number)
10560303999366736615…57740842968060231681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.112 Γ— 10⁹⁡(96-digit number)
21120607998733473230…15481685936120463361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.224 Γ— 10⁹⁡(96-digit number)
42241215997466946460…30963371872240926721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.448 Γ— 10⁹⁡(96-digit number)
84482431994933892920…61926743744481853441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.689 Γ— 10⁹⁢(97-digit number)
16896486398986778584…23853487488963706881
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 2833150

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 6cdf6ffa29109bdb303c4afb302cd2cd161a694a590b219c9ae1ea592a2815d4

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 #2,833,150 on Chainz β†—
Circulating Supply:57,987,266 XPMΒ·at block #6,842,864 Β· updates every 60s
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