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Home/Chain Registry/Block #2,833,352

Block #2,833,352

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2018, 4:40:17 PM Β· Difficulty 11.7154 Β· 4,008,481 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5f13efef96d048ea3a34a5be3e334e8bb4dd40d5f6ab63333fe2ea57f53845d2
View on Chainz β†—

Difficulty

11.715424

Transactions

1

Size

200 B

Version

2

Bits

0bb72604

Nonce

136,261,690

Timestamp

9/10/2018, 4:40:17 PM

Confirmations

4,008,481

Merkle Root

440af70f8f587d42dc1114b62f807d6ebd7935c6fcd7c1c858b3c5372b747a27
Transactions (1)
Coinbase440af70f8f587d…b3c5372b747a27
1 in β†’ 1 out7.2700 XPM110 B
ANowF2FW…CFDBZxeW
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.

4.928 Γ— 10⁹⁴(95-digit number)
49286004996695738536…63227320334159278080
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
4.928 Γ— 10⁹⁴(95-digit number)
49286004996695738536…63227320334159278081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.857 Γ— 10⁹⁴(95-digit number)
98572009993391477073…26454640668318556161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.971 Γ— 10⁹⁡(96-digit number)
19714401998678295414…52909281336637112321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.942 Γ— 10⁹⁡(96-digit number)
39428803997356590829…05818562673274224641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.885 Γ— 10⁹⁡(96-digit number)
78857607994713181658…11637125346548449281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.577 Γ— 10⁹⁢(97-digit number)
15771521598942636331…23274250693096898561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.154 Γ— 10⁹⁢(97-digit number)
31543043197885272663…46548501386193797121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.308 Γ— 10⁹⁢(97-digit number)
63086086395770545326…93097002772387594241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.261 Γ— 10⁹⁷(98-digit number)
12617217279154109065…86194005544775188481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.523 Γ— 10⁹⁷(98-digit number)
25234434558308218130…72388011089550376961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.046 Γ— 10⁹⁷(98-digit number)
50468869116616436261…44776022179100753921
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 2833352

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 5f13efef96d048ea3a34a5be3e334e8bb4dd40d5f6ab63333fe2ea57f53845d2

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 #2,833,352 on Chainz β†—
Circulating Supply:57,979,037 XPMΒ·at block #6,841,832 Β· updates every 60s
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