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Home/Chain Registry/Block #2,716,496

Block #2,716,496

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/22/2018, 1:32:30 PM Β· Difficulty 11.6146 Β· 4,116,887 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b46cd0fd2143ff49d8fb4a1b9f03633e351448b09fef02f760688b77a055308e
View on Chainz β†—

Difficulty

11.614569

Transactions

1

Size

200 B

Version

2

Bits

0b9d5464

Nonce

679,817,845

Timestamp

6/22/2018, 1:32:30 PM

Confirmations

4,116,887

Merkle Root

20edd2ec1456c2ab1a18c8905efadea59a80347b610ee1a9bb2aec1c2b6c8292
Transactions (1)
Coinbase20edd2ec1456c2…2aec1c2b6c8292
1 in β†’ 1 out7.4000 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.

2.117 Γ— 10⁹⁡(96-digit number)
21171039378667707951…45147016488810350560
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.117 Γ— 10⁹⁡(96-digit number)
21171039378667707951…45147016488810350559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.234 Γ— 10⁹⁡(96-digit number)
42342078757335415903…90294032977620701119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.468 Γ— 10⁹⁡(96-digit number)
84684157514670831807…80588065955241402239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.693 Γ— 10⁹⁢(97-digit number)
16936831502934166361…61176131910482804479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.387 Γ— 10⁹⁢(97-digit number)
33873663005868332723…22352263820965608959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.774 Γ— 10⁹⁢(97-digit number)
67747326011736665446…44704527641931217919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.354 Γ— 10⁹⁷(98-digit number)
13549465202347333089…89409055283862435839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.709 Γ— 10⁹⁷(98-digit number)
27098930404694666178…78818110567724871679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.419 Γ— 10⁹⁷(98-digit number)
54197860809389332356…57636221135449743359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.083 Γ— 10⁹⁸(99-digit number)
10839572161877866471…15272442270899486719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.167 Γ— 10⁹⁸(99-digit number)
21679144323755732942…30544884541798973439
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2716496

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 b46cd0fd2143ff49d8fb4a1b9f03633e351448b09fef02f760688b77a055308e

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 #2,716,496 on Chainz β†—
Circulating Supply:57,911,262 XPMΒ·at block #6,833,382 Β· updates every 60s
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