XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,277,303

Block #2,277,303

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/1/2017, 5:22:43 AM Β· Difficulty 10.9552 Β· 4,556,458 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ccde61ab531ef3083b87909dc9c9a0d1b251f4b89cb20c9637cb4c9c4567448b
View on Chainz β†—

Difficulty

10.955220

Transactions

1

Size

242 B

Version

2

Bits

0af4894e

Nonce

1,338,487,323

Timestamp

9/1/2017, 5:22:43 AM

Confirmations

4,556,458

Merkle Root

e9623a188e7694b0f02479961032242b6a769384f825de7dbfbaac1ee1c29a58
Transactions (1)
Coinbasee9623a188e7694…baac1ee1c29a58
1 in β†’ 2 out8.3200 XPM152 B
AdVLhe2j…QVKRTK6uALPu3s2c…EJXLjVFh
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.

1.735 Γ— 10⁹⁡(96-digit number)
17352764151222096671…65215779215398976420
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
1.735 Γ— 10⁹⁡(96-digit number)
17352764151222096671…65215779215398976419
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.470 Γ— 10⁹⁡(96-digit number)
34705528302444193343…30431558430797952839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.941 Γ— 10⁹⁡(96-digit number)
69411056604888386686…60863116861595905679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.388 Γ— 10⁹⁢(97-digit number)
13882211320977677337…21726233723191811359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.776 Γ— 10⁹⁢(97-digit number)
27764422641955354674…43452467446383622719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.552 Γ— 10⁹⁢(97-digit number)
55528845283910709349…86904934892767245439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.110 Γ— 10⁹⁷(98-digit number)
11105769056782141869…73809869785534490879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.221 Γ— 10⁹⁷(98-digit number)
22211538113564283739…47619739571068981759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.442 Γ— 10⁹⁷(98-digit number)
44423076227128567479…95239479142137963519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.884 Γ— 10⁹⁷(98-digit number)
88846152454257134959…90478958284275927039
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 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
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 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 2277303

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 ccde61ab531ef3083b87909dc9c9a0d1b251f4b89cb20c9637cb4c9c4567448b

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 #2,277,303 on Chainz β†—
Circulating Supply:57,914,305 XPMΒ·at block #6,833,760 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