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Home/Chain Registry/Block #2,796,420

Block #2,796,420

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/16/2018, 10:25:34 AM Β· Difficulty 11.6809 Β· 4,047,348 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f10fdd4288737178fb0bde76b6a6873da10557fd56409a9c674ecba8bd8c93ae
View on Chainz β†—

Difficulty

11.680882

Transactions

1

Size

199 B

Version

2

Bits

0bae4e45

Nonce

206,972,985

Timestamp

8/16/2018, 10:25:34 AM

Confirmations

4,047,348

Merkle Root

07cf1c15ce0eb4c47f110bfb1700b66650616af61b0663964f96da774fa43c62
Transactions (1)
Coinbase07cf1c15ce0eb4…96da774fa43c62
1 in β†’ 1 out7.3200 XPM109 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.

2.494 Γ— 10⁹⁴(95-digit number)
24946393099566716878…56984979196401112680
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
2.494 Γ— 10⁹⁴(95-digit number)
24946393099566716878…56984979196401112681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.989 Γ— 10⁹⁴(95-digit number)
49892786199133433756…13969958392802225361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.978 Γ— 10⁹⁴(95-digit number)
99785572398266867512…27939916785604450721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.995 Γ— 10⁹⁡(96-digit number)
19957114479653373502…55879833571208901441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.991 Γ— 10⁹⁡(96-digit number)
39914228959306747004…11759667142417802881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.982 Γ— 10⁹⁡(96-digit number)
79828457918613494009…23519334284835605761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.596 Γ— 10⁹⁢(97-digit number)
15965691583722698801…47038668569671211521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.193 Γ— 10⁹⁢(97-digit number)
31931383167445397603…94077337139342423041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.386 Γ— 10⁹⁢(97-digit number)
63862766334890795207…88154674278684846081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.277 Γ— 10⁹⁷(98-digit number)
12772553266978159041…76309348557369692161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.554 Γ— 10⁹⁷(98-digit number)
25545106533956318083…52618697114739384321
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 2796420

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 f10fdd4288737178fb0bde76b6a6873da10557fd56409a9c674ecba8bd8c93ae

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 #2,796,420 on Chainz β†—
Circulating Supply:57,994,518 XPMΒ·at block #6,843,767 Β· updates every 60s
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