XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,670,350

Block #2,670,350

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/20/2018, 7:52:23 PM Β· Difficulty 11.6821 Β· 4,172,422 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ec3f327cfca7ffa0674dbf5562a9a87f5e6f3b9faa552434c06efdb4638ca5d0
View on Chainz β†—

Difficulty

11.682059

Transactions

1

Size

201 B

Version

2

Bits

0bae9b6d

Nonce

202,273,013

Timestamp

5/20/2018, 7:52:23 PM

Confirmations

4,172,422

Merkle Root

3ecb209149cd4d90b33f6920f685a8a7fb680600c878707c0b13e9afe4926e21
Transactions (1)
Coinbase3ecb209149cd4d…13e9afe4926e21
1 in β†’ 1 out7.3200 XPM110 B
AHTawiMf…hhHKSHj4
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.

1.357 Γ— 10⁹⁢(97-digit number)
13576964617118158539…58026087685202944000
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
1.357 Γ— 10⁹⁢(97-digit number)
13576964617118158539…58026087685202943999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.715 Γ— 10⁹⁢(97-digit number)
27153929234236317078…16052175370405887999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.430 Γ— 10⁹⁢(97-digit number)
54307858468472634157…32104350740811775999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.086 Γ— 10⁹⁷(98-digit number)
10861571693694526831…64208701481623551999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.172 Γ— 10⁹⁷(98-digit number)
21723143387389053662…28417402963247103999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.344 Γ— 10⁹⁷(98-digit number)
43446286774778107325…56834805926494207999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.689 Γ— 10⁹⁷(98-digit number)
86892573549556214651…13669611852988415999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.737 Γ— 10⁹⁸(99-digit number)
17378514709911242930…27339223705976831999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.475 Γ— 10⁹⁸(99-digit number)
34757029419822485860…54678447411953663999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.951 Γ— 10⁹⁸(99-digit number)
69514058839644971721…09356894823907327999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.390 Γ— 10⁹⁹(100-digit number)
13902811767928994344…18713789647814655999
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 2670350

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 ec3f327cfca7ffa0674dbf5562a9a87f5e6f3b9faa552434c06efdb4638ca5d0

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 #2,670,350 on Chainz β†—
Circulating Supply:57,986,514 XPMΒ·at block #6,842,771 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy