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Home/Chain Registry/Block #2,636,874

Block #2,636,874

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/29/2018, 6:01:08 PM Β· Difficulty 11.4069 Β· 4,202,882 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
416a9015ca14302db3a84118677895fd9ef878a2c0f900a8074df4436229c470
View on Chainz β†—

Difficulty

11.406852

Transactions

1

Size

199 B

Version

2

Bits

0b682771

Nonce

114,356,627

Timestamp

4/29/2018, 6:01:08 PM

Confirmations

4,202,882

Merkle Root

84a599c6df9325449923613fa2650316675518e63c0273671d2753ac800455b4
Transactions (1)
Coinbase84a599c6df9325…2753ac800455b4
1 in β†’ 1 out7.6700 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.

5.888 Γ— 10⁹²(93-digit number)
58880101732443666252…38033759142734603040
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
5.888 Γ— 10⁹²(93-digit number)
58880101732443666252…38033759142734603039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.177 Γ— 10⁹³(94-digit number)
11776020346488733250…76067518285469206079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.355 Γ— 10⁹³(94-digit number)
23552040692977466501…52135036570938412159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.710 Γ— 10⁹³(94-digit number)
47104081385954933002…04270073141876824319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.420 Γ— 10⁹³(94-digit number)
94208162771909866004…08540146283753648639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.884 Γ— 10⁹⁴(95-digit number)
18841632554381973200…17080292567507297279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.768 Γ— 10⁹⁴(95-digit number)
37683265108763946401…34160585135014594559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.536 Γ— 10⁹⁴(95-digit number)
75366530217527892803…68321170270029189119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.507 Γ— 10⁹⁡(96-digit number)
15073306043505578560…36642340540058378239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.014 Γ— 10⁹⁡(96-digit number)
30146612087011157121…73284681080116756479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.029 Γ— 10⁹⁡(96-digit number)
60293224174022314242…46569362160233512959
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 2636874

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 416a9015ca14302db3a84118677895fd9ef878a2c0f900a8074df4436229c470

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 #2,636,874 on Chainz β†—
Circulating Supply:57,962,335 XPMΒ·at block #6,839,755 Β· updates every 60s
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