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Home/Chain Registry/Block #2,948,667

Block #2,948,667

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/2/2018, 10:10:59 AM Β· Difficulty 11.3999 Β· 3,885,093 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
955d99c5bb948bcc811bbafd5f317c7396db031bcbbfb8b071be1618cf1b6b6c
View on Chainz β†—

Difficulty

11.399933

Transactions

1

Size

200 B

Version

2

Bits

0b666209

Nonce

1,992,813,168

Timestamp

12/2/2018, 10:10:59 AM

Confirmations

3,885,093

Merkle Root

58d32b530fcc499c429ce1aaf0c8fa8f27097529ff0e4c704b86306db20e5f4e
Transactions (1)
Coinbase58d32b530fcc49…86306db20e5f4e
1 in β†’ 1 out7.6800 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.

5.248 Γ— 10⁹³(94-digit number)
52484843892937599446…04743581211343764260
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
5.248 Γ— 10⁹³(94-digit number)
52484843892937599446…04743581211343764261
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.049 Γ— 10⁹⁴(95-digit number)
10496968778587519889…09487162422687528521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.099 Γ— 10⁹⁴(95-digit number)
20993937557175039778…18974324845375057041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.198 Γ— 10⁹⁴(95-digit number)
41987875114350079556…37948649690750114081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.397 Γ— 10⁹⁴(95-digit number)
83975750228700159113…75897299381500228161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.679 Γ— 10⁹⁡(96-digit number)
16795150045740031822…51794598763000456321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.359 Γ— 10⁹⁡(96-digit number)
33590300091480063645…03589197526000912641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.718 Γ— 10⁹⁡(96-digit number)
67180600182960127290…07178395052001825281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.343 Γ— 10⁹⁢(97-digit number)
13436120036592025458…14356790104003650561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.687 Γ— 10⁹⁢(97-digit number)
26872240073184050916…28713580208007301121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.374 Γ— 10⁹⁢(97-digit number)
53744480146368101832…57427160416014602241
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 2948667

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 955d99c5bb948bcc811bbafd5f317c7396db031bcbbfb8b071be1618cf1b6b6c

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 #2,948,667 on Chainz β†—
Circulating Supply:57,914,297 XPMΒ·at block #6,833,759 Β· updates every 60s
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