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Home/Chain Registry/Block #2,633,809

Block #2,633,809

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 3:06:21 PM Β· Difficulty 11.2090 Β· 4,208,585 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
67b610687ff46296ffe5759347a94eeb1ef28f1753d973edea7c32042ebc03da
View on Chainz β†—

Difficulty

11.209048

Transactions

2

Size

575 B

Version

2

Bits

0b358428

Nonce

149,935,650

Timestamp

4/28/2018, 3:06:21 PM

Confirmations

4,208,585

Merkle Root

30374da37b7d379c2f758fb6549cd0a623da2a2cb374d8b3888c2b90a1386aa8
Transactions (2)
Coinbase5ce0831f077a1c…6c9d070a168cc1
1 in β†’ 1 out7.9600 XPM110 B
Adqah8zh…1WwoHJ9t
e335890070904f…0bcbc70cbcbcf8
2 in β†’ 2 out5.8422 XPM375 B
APJSnDKS…dDPHqj6CAWp4iAg7…FUBLEm8x
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.

1.047 Γ— 10⁹⁡(96-digit number)
10471294369354613380…05370994183245404160
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
1.047 Γ— 10⁹⁡(96-digit number)
10471294369354613380…05370994183245404161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.094 Γ— 10⁹⁡(96-digit number)
20942588738709226761…10741988366490808321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.188 Γ— 10⁹⁡(96-digit number)
41885177477418453523…21483976732981616641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.377 Γ— 10⁹⁡(96-digit number)
83770354954836907046…42967953465963233281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.675 Γ— 10⁹⁢(97-digit number)
16754070990967381409…85935906931926466561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.350 Γ— 10⁹⁢(97-digit number)
33508141981934762818…71871813863852933121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.701 Γ— 10⁹⁢(97-digit number)
67016283963869525637…43743627727705866241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.340 Γ— 10⁹⁷(98-digit number)
13403256792773905127…87487255455411732481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.680 Γ— 10⁹⁷(98-digit number)
26806513585547810254…74974510910823464961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.361 Γ— 10⁹⁷(98-digit number)
53613027171095620509…49949021821646929921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.072 Γ— 10⁹⁸(99-digit number)
10722605434219124101…99898043643293859841
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 2633809

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 67b610687ff46296ffe5759347a94eeb1ef28f1753d973edea7c32042ebc03da

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 #2,633,809 on Chainz β†—
Circulating Supply:57,983,563 XPMΒ·at block #6,842,393 Β· updates every 60s
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