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Home/Chain Registry/Block #2,646,606

Block #2,646,606

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 11:07:43 AM Β· Difficulty 11.7518 Β· 4,197,803 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f1e1531f8bb6c39fd2d2b717e1c48b777b0c9c8a1dc5c35242b36cdf11af5849
View on Chainz β†—

Difficulty

11.751776

Transactions

1

Size

201 B

Version

2

Bits

0bc0746a

Nonce

199,481,245

Timestamp

5/3/2018, 11:07:43 AM

Confirmations

4,197,803

Merkle Root

b6b304525141a4c5aac7d234f57996de0e15c1e78ef934702a9b97f3a381bb86
Transactions (1)
Coinbaseb6b304525141a4…9b97f3a381bb86
1 in β†’ 1 out7.2300 XPM110 B
ALhYXmRA…DwpcNijS
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.

7.644 Γ— 10⁹⁡(96-digit number)
76443783990307038559…46311602267914287360
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
7.644 Γ— 10⁹⁡(96-digit number)
76443783990307038559…46311602267914287361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.528 Γ— 10⁹⁢(97-digit number)
15288756798061407711…92623204535828574721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.057 Γ— 10⁹⁢(97-digit number)
30577513596122815423…85246409071657149441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.115 Γ— 10⁹⁢(97-digit number)
61155027192245630847…70492818143314298881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.223 Γ— 10⁹⁷(98-digit number)
12231005438449126169…40985636286628597761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.446 Γ— 10⁹⁷(98-digit number)
24462010876898252339…81971272573257195521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.892 Γ— 10⁹⁷(98-digit number)
48924021753796504678…63942545146514391041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.784 Γ— 10⁹⁷(98-digit number)
97848043507593009356…27885090293028782081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.956 Γ— 10⁹⁸(99-digit number)
19569608701518601871…55770180586057564161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.913 Γ— 10⁹⁸(99-digit number)
39139217403037203742…11540361172115128321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.827 Γ— 10⁹⁸(99-digit number)
78278434806074407485…23080722344230256641
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 2646606

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 f1e1531f8bb6c39fd2d2b717e1c48b777b0c9c8a1dc5c35242b36cdf11af5849

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 #2,646,606 on Chainz β†—
Circulating Supply:57,999,665 XPMΒ·at block #6,844,408 Β· updates every 60s
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