XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,961,778

Block #2,961,778

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/11/2018, 8:14:48 PM Β· Difficulty 11.3441 Β· 3,869,508 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
348619ab6df62f724acb6a477a48705924c463c400dc8053c99a22fed24a1c92
View on Chainz β†—

Difficulty

11.344061

Transactions

2

Size

575 B

Version

2

Bits

0b581460

Nonce

1,980,790,277

Timestamp

12/11/2018, 8:14:48 PM

Confirmations

3,869,508

Merkle Root

b3681e504add979bc967414f0673a53b6632c508e6db4781b04d954fe4cc2548
Transactions (2)
Coinbasedb44abceeece5e…678dc8e1088340
1 in β†’ 1 out7.7700 XPM110 B
AbXwmGxD…4XXYP765
947b8dc231a663…0b6812d74fc271
2 in β†’ 2 out257.2230 XPM374 B
AbKFvGKV…eL3bdfEbAJqPR4x9…iEcrqUV7
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.

1.191 Γ— 10⁹⁢(97-digit number)
11915567686385194285…93716610439325450240
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
1.191 Γ— 10⁹⁢(97-digit number)
11915567686385194285…93716610439325450239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.383 Γ— 10⁹⁢(97-digit number)
23831135372770388571…87433220878650900479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.766 Γ— 10⁹⁢(97-digit number)
47662270745540777142…74866441757301800959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.532 Γ— 10⁹⁢(97-digit number)
95324541491081554285…49732883514603601919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.906 Γ— 10⁹⁷(98-digit number)
19064908298216310857…99465767029207203839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.812 Γ— 10⁹⁷(98-digit number)
38129816596432621714…98931534058414407679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.625 Γ— 10⁹⁷(98-digit number)
76259633192865243428…97863068116828815359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.525 Γ— 10⁹⁸(99-digit number)
15251926638573048685…95726136233657630719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.050 Γ— 10⁹⁸(99-digit number)
30503853277146097371…91452272467315261439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.100 Γ— 10⁹⁸(99-digit number)
61007706554292194742…82904544934630522879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.220 Γ— 10⁹⁹(100-digit number)
12201541310858438948…65809089869261045759
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 2961778

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 348619ab6df62f724acb6a477a48705924c463c400dc8053c99a22fed24a1c92

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 #2,961,778 on Chainz β†—
Circulating Supply:57,894,433 XPMΒ·at block #6,831,285 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