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Block #2,640,648

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2018, 1:55:25 AM Β· Difficulty 11.5900 Β· 4,192,892 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ac03a1a48d6b700ce758899740409a234b453b3488076dc9c6dcaa59d2ec365e
View on Chainz β†—

Difficulty

11.589969

Transactions

1

Size

199 B

Version

2

Bits

0b97083b

Nonce

246,237,151

Timestamp

5/1/2018, 1:55:25 AM

Confirmations

4,192,892

Merkle Root

e215bcc3f79bebc61077b567883b3890bd3497774e86d31bf930c17f760401a1
Transactions (1)
Coinbasee215bcc3f79beb…30c17f760401a1
1 in β†’ 1 out7.4300 XPM110 B
Adqah8zh…1WwoHJ9t
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.

3.044 Γ— 10⁹³(94-digit number)
30442765759445700586…88972641004425344740
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
3.044 Γ— 10⁹³(94-digit number)
30442765759445700586…88972641004425344739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.088 Γ— 10⁹³(94-digit number)
60885531518891401173…77945282008850689479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.217 Γ— 10⁹⁴(95-digit number)
12177106303778280234…55890564017701378959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.435 Γ— 10⁹⁴(95-digit number)
24354212607556560469…11781128035402757919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.870 Γ— 10⁹⁴(95-digit number)
48708425215113120939…23562256070805515839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.741 Γ— 10⁹⁴(95-digit number)
97416850430226241878…47124512141611031679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.948 Γ— 10⁹⁡(96-digit number)
19483370086045248375…94249024283222063359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.896 Γ— 10⁹⁡(96-digit number)
38966740172090496751…88498048566444126719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.793 Γ— 10⁹⁡(96-digit number)
77933480344180993502…76996097132888253439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.558 Γ— 10⁹⁢(97-digit number)
15586696068836198700…53992194265776506879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.117 Γ— 10⁹⁢(97-digit number)
31173392137672397400…07984388531553013759
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 2640648

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 ac03a1a48d6b700ce758899740409a234b453b3488076dc9c6dcaa59d2ec365e

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 #2,640,648 on Chainz β†—
Circulating Supply:57,912,520 XPMΒ·at block #6,833,539 Β· updates every 60s
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