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Home/Chain Registry/Block #2,634,060

Block #2,634,060

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/28/2018, 6:03:07 PM Β· Difficulty 11.2205 Β· 4,202,840 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9d74c8b5a57252a1c0127d05a75683e21d04d5e56f94d97eb0a16f2ad0422b35
View on Chainz β†—

Difficulty

11.220546

Transactions

1

Size

200 B

Version

2

Bits

0b3875af

Nonce

63,708,014

Timestamp

4/28/2018, 6:03:07 PM

Confirmations

4,202,840

Merkle Root

ed19aba8b1bb1b90eaeefbc2574b7ea3616944bb27c839945376a4ef86dc84b7
Transactions (1)
Coinbaseed19aba8b1bb1b…76a4ef86dc84b7
1 in β†’ 1 out7.9300 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.

2.619 Γ— 10⁹⁡(96-digit number)
26196703062867865814…35738438807961456640
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
2.619 Γ— 10⁹⁡(96-digit number)
26196703062867865814…35738438807961456639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.239 Γ— 10⁹⁡(96-digit number)
52393406125735731629…71476877615922913279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.047 Γ— 10⁹⁢(97-digit number)
10478681225147146325…42953755231845826559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.095 Γ— 10⁹⁢(97-digit number)
20957362450294292651…85907510463691653119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.191 Γ— 10⁹⁢(97-digit number)
41914724900588585303…71815020927383306239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.382 Γ— 10⁹⁢(97-digit number)
83829449801177170607…43630041854766612479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.676 Γ— 10⁹⁷(98-digit number)
16765889960235434121…87260083709533224959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.353 Γ— 10⁹⁷(98-digit number)
33531779920470868242…74520167419066449919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.706 Γ— 10⁹⁷(98-digit number)
67063559840941736485…49040334838132899839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.341 Γ— 10⁹⁸(99-digit number)
13412711968188347297…98080669676265799679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.682 Γ— 10⁹⁸(99-digit number)
26825423936376694594…96161339352531599359
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 2634060

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 9d74c8b5a57252a1c0127d05a75683e21d04d5e56f94d97eb0a16f2ad0422b35

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 #2,634,060 on Chainz β†—
Circulating Supply:57,939,491 XPMΒ·at block #6,836,899 Β· updates every 60s
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