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Home/Chain Registry/Block #2,803,533

Block #2,803,533

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/21/2018, 12:54:18 PM Β· Difficulty 11.6659 Β· 4,036,917 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1e3f3bd981b60671d467fbf084c0de3f3271971f00d480b9f20a1e26df88282d
View on Chainz β†—

Difficulty

11.665947

Transactions

3

Size

651 B

Version

2

Bits

0baa7b82

Nonce

1,129,168,445

Timestamp

8/21/2018, 12:54:18 PM

Confirmations

4,036,917

Merkle Root

e443620ad16fb47df07ad2f23a30066091370404d2f700683dd928428884da8d
Transactions (3)
Coinbase09e683fc279ada…39738be1edfcd5
1 in β†’ 1 out7.3600 XPM110 B
AZtxQr2F…7grUWrUz
741289c94fd159…c83fc1adb42420
1 in β†’ 2 out2.6786 XPM226 B
AVDnPg3b…rkuNnYdHAV3JM4zu…4Yqk98pg
eccea4a0870480…ca9fcf72eb505e
1 in β†’ 2 out2.3469 XPM225 B
ANCrhkse…k4RkT49MANjTQp24…sVkz8Xup
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.

2.040 Γ— 10⁹⁴(95-digit number)
20407322675535378979…10988789081656336000
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
2.040 Γ— 10⁹⁴(95-digit number)
20407322675535378979…10988789081656336001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.081 Γ— 10⁹⁴(95-digit number)
40814645351070757959…21977578163312672001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.162 Γ— 10⁹⁴(95-digit number)
81629290702141515918…43955156326625344001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.632 Γ— 10⁹⁡(96-digit number)
16325858140428303183…87910312653250688001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.265 Γ— 10⁹⁡(96-digit number)
32651716280856606367…75820625306501376001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.530 Γ— 10⁹⁡(96-digit number)
65303432561713212734…51641250613002752001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.306 Γ— 10⁹⁢(97-digit number)
13060686512342642546…03282501226005504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.612 Γ— 10⁹⁢(97-digit number)
26121373024685285093…06565002452011008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.224 Γ— 10⁹⁢(97-digit number)
52242746049370570187…13130004904022016001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.044 Γ— 10⁹⁷(98-digit number)
10448549209874114037…26260009808044032001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.089 Γ— 10⁹⁷(98-digit number)
20897098419748228075…52520019616088064001
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 2803533

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 1e3f3bd981b60671d467fbf084c0de3f3271971f00d480b9f20a1e26df88282d

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 #2,803,533 on Chainz β†—
Circulating Supply:57,967,930 XPMΒ·at block #6,840,449 Β· updates every 60s
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