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Block #2,803,292

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/21/2018, 8:55:41 AM Β· Difficulty 11.6657 Β· 4,038,123 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f4b974f4333bf00d15d76494c77d191f51502a5fa95502c23dbba31cd3d48711
View on Chainz β†—

Difficulty

11.665707

Transactions

1

Size

200 B

Version

2

Bits

0baa6bc8

Nonce

131,147,110

Timestamp

8/21/2018, 8:55:41 AM

Confirmations

4,038,123

Merkle Root

debee02adf193563ada0a956b8fb378c7e3f82f1c668cd59ad18a4bf0d8c95c4
Transactions (1)
Coinbasedebee02adf1935…18a4bf0d8c95c4
1 in β†’ 1 out7.3400 XPM110 B
ALoADQo6…nsYBux6b
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.

1.348 Γ— 10⁹⁴(95-digit number)
13482519181755215199…96652114328422388150
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
1.348 Γ— 10⁹⁴(95-digit number)
13482519181755215199…96652114328422388151
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.696 Γ— 10⁹⁴(95-digit number)
26965038363510430398…93304228656844776301
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.393 Γ— 10⁹⁴(95-digit number)
53930076727020860796…86608457313689552601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.078 Γ— 10⁹⁡(96-digit number)
10786015345404172159…73216914627379105201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.157 Γ— 10⁹⁡(96-digit number)
21572030690808344318…46433829254758210401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.314 Γ— 10⁹⁡(96-digit number)
43144061381616688637…92867658509516420801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.628 Γ— 10⁹⁡(96-digit number)
86288122763233377274…85735317019032841601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.725 Γ— 10⁹⁢(97-digit number)
17257624552646675454…71470634038065683201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.451 Γ— 10⁹⁢(97-digit number)
34515249105293350909…42941268076131366401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.903 Γ— 10⁹⁢(97-digit number)
69030498210586701819…85882536152262732801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.380 Γ— 10⁹⁷(98-digit number)
13806099642117340363…71765072304525465601
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 2803292

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 f4b974f4333bf00d15d76494c77d191f51502a5fa95502c23dbba31cd3d48711

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 #2,803,292 on Chainz β†—
Circulating Supply:57,975,695 XPMΒ·at block #6,841,414 Β· updates every 60s
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