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Block #2,468,630

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/11/2018, 11:05:55 PM Β· Difficulty 10.9601 Β· 4,372,839 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
de84cd91a6d772b3d136a7095f2bec6407440f3c88cc043b185ec0f3281cddfd
View on Chainz β†—

Difficulty

10.960087

Transactions

2

Size

574 B

Version

2

Bits

0af5c83c

Nonce

853,616,187

Timestamp

1/11/2018, 11:05:55 PM

Confirmations

4,372,839

Merkle Root

a8e158d631866a1505fa935104f811f61081c3d5c4a0ffa13291675d9f72c4c9
Transactions (2)
Coinbase732dc639ddd0fd…14ffab47d4510f
1 in β†’ 1 out8.3200 XPM110 B
AaF25Ute…pxcoZYGm
370089822a1998…1600af7f0d939a
2 in β†’ 2 out678.0745 XPM374 B
AeE8jzQC…xaMsk2EKANs8fHEc…WA6WXndi
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.

3.355 Γ— 10⁹⁴(95-digit number)
33556303103123436455…08183506483210117760
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
3.355 Γ— 10⁹⁴(95-digit number)
33556303103123436455…08183506483210117761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.711 Γ— 10⁹⁴(95-digit number)
67112606206246872911…16367012966420235521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.342 Γ— 10⁹⁡(96-digit number)
13422521241249374582…32734025932840471041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.684 Γ— 10⁹⁡(96-digit number)
26845042482498749164…65468051865680942081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.369 Γ— 10⁹⁡(96-digit number)
53690084964997498329…30936103731361884161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.073 Γ— 10⁹⁢(97-digit number)
10738016992999499665…61872207462723768321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.147 Γ— 10⁹⁢(97-digit number)
21476033985998999331…23744414925447536641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.295 Γ— 10⁹⁢(97-digit number)
42952067971997998663…47488829850895073281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.590 Γ— 10⁹⁢(97-digit number)
85904135943995997326…94977659701790146561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.718 Γ— 10⁹⁷(98-digit number)
17180827188799199465…89955319403580293121
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 2468630

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 de84cd91a6d772b3d136a7095f2bec6407440f3c88cc043b185ec0f3281cddfd

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 #2,468,630 on Chainz β†—
Circulating Supply:57,976,126 XPMΒ·at block #6,841,468 Β· updates every 60s
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