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Home/Chain Registry/Block #2,076,288

Block #2,076,288

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/18/2017, 3:39:21 PM Β· Difficulty 10.8456 Β· 4,769,407 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
88a40ef41424839d61643e334f75ed6eacdc1caea27465e45bb05873c3248974
View on Chainz β†—

Difficulty

10.845640

Transactions

1

Size

200 B

Version

2

Bits

0ad87be1

Nonce

912,210,723

Timestamp

4/18/2017, 3:39:21 PM

Confirmations

4,769,407

Merkle Root

058bd9869bf29ad2d1671399c8cc0ed189f74fffd87acf31be6251a72b1a4fe1
Transactions (1)
Coinbase058bd9869bf29a…6251a72b1a4fe1
1 in β†’ 1 out8.4900 XPM110 B
AGStDvkm…P144F9CY
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.

2.392 Γ— 10⁹⁴(95-digit number)
23923731581915888896…75301670412562579680
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
2.392 Γ— 10⁹⁴(95-digit number)
23923731581915888896…75301670412562579679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.784 Γ— 10⁹⁴(95-digit number)
47847463163831777792…50603340825125159359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.569 Γ— 10⁹⁴(95-digit number)
95694926327663555585…01206681650250318719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.913 Γ— 10⁹⁡(96-digit number)
19138985265532711117…02413363300500637439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.827 Γ— 10⁹⁡(96-digit number)
38277970531065422234…04826726601001274879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.655 Γ— 10⁹⁡(96-digit number)
76555941062130844468…09653453202002549759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.531 Γ— 10⁹⁢(97-digit number)
15311188212426168893…19306906404005099519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.062 Γ— 10⁹⁢(97-digit number)
30622376424852337787…38613812808010199039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.124 Γ— 10⁹⁢(97-digit number)
61244752849704675575…77227625616020398079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.224 Γ— 10⁹⁷(98-digit number)
12248950569940935115…54455251232040796159
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 2076288

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 88a40ef41424839d61643e334f75ed6eacdc1caea27465e45bb05873c3248974

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 #2,076,288 on Chainz β†—
Circulating Supply:58,010,017 XPMΒ·at block #6,845,694 Β· updates every 60s
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