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Block #2,283,418

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/5/2017, 10:59:17 AM Β· Difficulty 10.9556 Β· 4,548,037 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
86905777a6e2d138baf592c04d25d8343aedfb06e65bc980097075483bdef659
View on Chainz β†—

Difficulty

10.955572

Transactions

2

Size

916 B

Version

2

Bits

0af4a05d

Nonce

231,672,545

Timestamp

9/5/2017, 10:59:17 AM

Confirmations

4,548,037

Merkle Root

c26a0fdf23bc80d14b2558706c66daa96ed3ebebdf77716a03698d9d8c6ba1f8
Transactions (2)
Coinbase6d042b238ae872…0123887c72e9e0
1 in β†’ 1 out8.3400 XPM109 B
ATotY5AG…2c39yhWy
ea79cbf632e4e2…b11a9fc73baf8e
5 in β†’ 1 out24.0000 XPM717 B
ARezZb4y…FxP7ivbi
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.

1.537 Γ— 10⁹⁡(96-digit number)
15377647038849604406…13122116853205091520
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
1.537 Γ— 10⁹⁡(96-digit number)
15377647038849604406…13122116853205091521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.075 Γ— 10⁹⁡(96-digit number)
30755294077699208812…26244233706410183041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.151 Γ— 10⁹⁡(96-digit number)
61510588155398417624…52488467412820366081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.230 Γ— 10⁹⁢(97-digit number)
12302117631079683524…04976934825640732161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.460 Γ— 10⁹⁢(97-digit number)
24604235262159367049…09953869651281464321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.920 Γ— 10⁹⁢(97-digit number)
49208470524318734099…19907739302562928641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.841 Γ— 10⁹⁢(97-digit number)
98416941048637468199…39815478605125857281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.968 Γ— 10⁹⁷(98-digit number)
19683388209727493639…79630957210251714561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.936 Γ— 10⁹⁷(98-digit number)
39366776419454987279…59261914420503429121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.873 Γ— 10⁹⁷(98-digit number)
78733552838909974559…18523828841006858241
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2283418

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 86905777a6e2d138baf592c04d25d8343aedfb06e65bc980097075483bdef659

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 #2,283,418 on Chainz β†—
Circulating Supply:57,895,779 XPMΒ·at block #6,831,454 Β· updates every 60s
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