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Home/Chain Registry/Block #2,699,340

Block #2,699,340

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/10/2018, 8:44:14 AM Β· Difficulty 11.6443 Β· 4,142,927 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f74a23f2c2833878b3c15bd5a1db218fb8e51760ef0684fe0aa19701d48ab5a8
View on Chainz β†—

Difficulty

11.644325

Transactions

1

Size

200 B

Version

2

Bits

0ba4f280

Nonce

2,143,818,427

Timestamp

6/10/2018, 8:44:14 AM

Confirmations

4,142,927

Merkle Root

0d37fe2a7acaa4926f18e622712d8af913f4b29a41aad7a2d51403008fcfe4fb
Transactions (1)
Coinbase0d37fe2a7acaa4…1403008fcfe4fb
1 in β†’ 1 out7.3600 XPM110 B
AaNsHTbc…aHdBTD7L
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.

4.289 Γ— 10⁹³(94-digit number)
42891513312956669810…24667561173741145600
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
4.289 Γ— 10⁹³(94-digit number)
42891513312956669810…24667561173741145601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.578 Γ— 10⁹³(94-digit number)
85783026625913339620…49335122347482291201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.715 Γ— 10⁹⁴(95-digit number)
17156605325182667924…98670244694964582401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.431 Γ— 10⁹⁴(95-digit number)
34313210650365335848…97340489389929164801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.862 Γ— 10⁹⁴(95-digit number)
68626421300730671696…94680978779858329601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.372 Γ— 10⁹⁡(96-digit number)
13725284260146134339…89361957559716659201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.745 Γ— 10⁹⁡(96-digit number)
27450568520292268678…78723915119433318401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.490 Γ— 10⁹⁡(96-digit number)
54901137040584537357…57447830238866636801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.098 Γ— 10⁹⁢(97-digit number)
10980227408116907471…14895660477733273601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.196 Γ— 10⁹⁢(97-digit number)
21960454816233814942…29791320955466547201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.392 Γ— 10⁹⁢(97-digit number)
43920909632467629885…59582641910933094401
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 2699340

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 f74a23f2c2833878b3c15bd5a1db218fb8e51760ef0684fe0aa19701d48ab5a8

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 #2,699,340 on Chainz β†—
Circulating Supply:57,982,535 XPMΒ·at block #6,842,266 Β· updates every 60s
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