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Home/Chain Registry/Block #2,685,795

Block #2,685,795

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/31/2018, 11:36:32 AM Β· Difficulty 11.6889 Β· 4,151,317 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9d3e8a5f8ec86572978910d0681de36c091fa4f2a2b2f0064d1a4b7427370caa
View on Chainz β†—

Difficulty

11.688894

Transactions

1

Size

200 B

Version

2

Bits

0bb05b5c

Nonce

19,058,164

Timestamp

5/31/2018, 11:36:32 AM

Confirmations

4,151,317

Merkle Root

eb8a87aefa972731dd08ed47b7a70eb616cf20302b84af3e8b0a58b47cd76111
Transactions (1)
Coinbaseeb8a87aefa9727…0a58b47cd76111
1 in β†’ 1 out7.3100 XPM110 B
AaGmmfZi…p4UUPrfa
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.

1.636 Γ— 10⁹⁴(95-digit number)
16367843918431430960…09380266783852304000
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.636 Γ— 10⁹⁴(95-digit number)
16367843918431430960…09380266783852303999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.273 Γ— 10⁹⁴(95-digit number)
32735687836862861920…18760533567704607999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.547 Γ— 10⁹⁴(95-digit number)
65471375673725723840…37521067135409215999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.309 Γ— 10⁹⁡(96-digit number)
13094275134745144768…75042134270818431999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.618 Γ— 10⁹⁡(96-digit number)
26188550269490289536…50084268541636863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.237 Γ— 10⁹⁡(96-digit number)
52377100538980579072…00168537083273727999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.047 Γ— 10⁹⁢(97-digit number)
10475420107796115814…00337074166547455999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.095 Γ— 10⁹⁢(97-digit number)
20950840215592231628…00674148333094911999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.190 Γ— 10⁹⁢(97-digit number)
41901680431184463257…01348296666189823999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.380 Γ— 10⁹⁢(97-digit number)
83803360862368926515…02696593332379647999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.676 Γ— 10⁹⁷(98-digit number)
16760672172473785303…05393186664759295999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2685795

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 9d3e8a5f8ec86572978910d0681de36c091fa4f2a2b2f0064d1a4b7427370caa

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 #2,685,795 on Chainz β†—
Circulating Supply:57,941,203 XPMΒ·at block #6,837,111 Β· updates every 60s
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