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Home/Chain Registry/Block #2,935,348

Block #2,935,348

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/23/2018, 5:25:49 AM Β· Difficulty 11.3904 Β· 3,907,751 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e6c66aea6006983d432f5ffba9e70e686be1988863ddad6f54c2df696077d67f
View on Chainz β†—

Difficulty

11.390375

Transactions

1

Size

200 B

Version

2

Bits

0b63efa5

Nonce

693,083,396

Timestamp

11/23/2018, 5:25:49 AM

Confirmations

3,907,751

Merkle Root

bb4fa62e83792c414e6b57401b03b7dac45086bd86a17a8fd1bf35a4858ca7be
Transactions (1)
Coinbasebb4fa62e83792c…bf35a4858ca7be
1 in β†’ 1 out7.6900 XPM110 B
AUhjokok…k5m93PZR
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.

4.995 Γ— 10⁹⁴(95-digit number)
49958115712629425509…85873528856629932940
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
4.995 Γ— 10⁹⁴(95-digit number)
49958115712629425509…85873528856629932941
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.991 Γ— 10⁹⁴(95-digit number)
99916231425258851019…71747057713259865881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.998 Γ— 10⁹⁡(96-digit number)
19983246285051770203…43494115426519731761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.996 Γ— 10⁹⁡(96-digit number)
39966492570103540407…86988230853039463521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.993 Γ— 10⁹⁡(96-digit number)
79932985140207080815…73976461706078927041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.598 Γ— 10⁹⁢(97-digit number)
15986597028041416163…47952923412157854081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.197 Γ— 10⁹⁢(97-digit number)
31973194056082832326…95905846824315708161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.394 Γ— 10⁹⁢(97-digit number)
63946388112165664652…91811693648631416321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.278 Γ— 10⁹⁷(98-digit number)
12789277622433132930…83623387297262832641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.557 Γ— 10⁹⁷(98-digit number)
25578555244866265861…67246774594525665281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.115 Γ— 10⁹⁷(98-digit number)
51157110489732531722…34493549189051330561
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 2935348

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 e6c66aea6006983d432f5ffba9e70e686be1988863ddad6f54c2df696077d67f

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 #2,935,348 on Chainz β†—
Circulating Supply:57,989,155 XPMΒ·at block #6,843,098 Β· updates every 60s
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