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Block #2,792,362

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/13/2018, 4:17:40 PM Β· Difficulty 11.6751 Β· 4,046,499 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8a8ce657fd3cd901c62e6963755da17d570ece3b91270acfa17ee660f95408eb
View on Chainz β†—

Difficulty

11.675093

Transactions

1

Size

201 B

Version

2

Bits

0bacd2ec

Nonce

743,942,589

Timestamp

8/13/2018, 4:17:40 PM

Confirmations

4,046,499

Merkle Root

0075f3a313b6bd6ad15fa07124a5593811d582bde9688ab06a28024a97ddd9d6
Transactions (1)
Coinbase0075f3a313b6bd…28024a97ddd9d6
1 in β†’ 1 out7.3200 XPM110 B
AZtxQr2F…7grUWrUz
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.

8.234 Γ— 10⁹⁡(96-digit number)
82343875495918843139…39470717528855521280
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
8.234 Γ— 10⁹⁡(96-digit number)
82343875495918843139…39470717528855521281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.646 Γ— 10⁹⁢(97-digit number)
16468775099183768627…78941435057711042561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.293 Γ— 10⁹⁢(97-digit number)
32937550198367537255…57882870115422085121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.587 Γ— 10⁹⁢(97-digit number)
65875100396735074511…15765740230844170241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.317 Γ— 10⁹⁷(98-digit number)
13175020079347014902…31531480461688340481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.635 Γ— 10⁹⁷(98-digit number)
26350040158694029804…63062960923376680961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.270 Γ— 10⁹⁷(98-digit number)
52700080317388059609…26125921846753361921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.054 Γ— 10⁹⁸(99-digit number)
10540016063477611921…52251843693506723841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.108 Γ— 10⁹⁸(99-digit number)
21080032126955223843…04503687387013447681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.216 Γ— 10⁹⁸(99-digit number)
42160064253910447687…09007374774026895361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.432 Γ— 10⁹⁸(99-digit number)
84320128507820895374…18014749548053790721
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 2792362

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 8a8ce657fd3cd901c62e6963755da17d570ece3b91270acfa17ee660f95408eb

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 #2,792,362 on Chainz β†—
Circulating Supply:57,955,153 XPMΒ·at block #6,838,860 Β· updates every 60s
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