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Home/Chain Registry/Block #2,633,775

Block #2,633,775

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 4/28/2018, 2:39:34 PM Β· Difficulty 11.2079 Β· 4,197,346 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
293dc37a2d0e537d733f5dfefa2dfc24cb96e609c76505bbe588cf10ec6edb0a
View on Chainz β†—

Difficulty

11.207861

Transactions

3

Size

654 B

Version

2

Bits

0b35365e

Nonce

1,209,467,706

Timestamp

4/28/2018, 2:39:34 PM

Confirmations

4,197,346

Merkle Root

36db031374b3010c7d8517c4f6cd7e0213a3b5cecb1d25b89c10e1d4a71db9de
Transactions (3)
Coinbasedcc81c3c256792…7585258b7da3d3
1 in β†’ 1 out7.9700 XPM110 B
Adqah8zh…1WwoHJ9t
59bb9673297dca…45ff02b67cd83d
1 in β†’ 2 out33646.2597 XPM227 B
AatWaB7p…QFc39RSoAY3jQmKf…5ruHM3GF
457442f5377668…dfc1f75890ac78
1 in β†’ 2 out272497.3109 XPM227 B
AGG8ABnf…1Xj2WxQrAJ3vgUCe…Y8x9MiP5
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.

4.858 Γ— 10⁹⁴(95-digit number)
48580377409972449715…48266496313526160000
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
4.858 Γ— 10⁹⁴(95-digit number)
48580377409972449715…48266496313526159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.716 Γ— 10⁹⁴(95-digit number)
97160754819944899430…96532992627052319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.943 Γ— 10⁹⁡(96-digit number)
19432150963988979886…93065985254104639999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.886 Γ— 10⁹⁡(96-digit number)
38864301927977959772…86131970508209279999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.772 Γ— 10⁹⁡(96-digit number)
77728603855955919544…72263941016418559999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.554 Γ— 10⁹⁢(97-digit number)
15545720771191183908…44527882032837119999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.109 Γ— 10⁹⁢(97-digit number)
31091441542382367817…89055764065674239999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.218 Γ— 10⁹⁢(97-digit number)
62182883084764735635…78111528131348479999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.243 Γ— 10⁹⁷(98-digit number)
12436576616952947127…56223056262696959999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.487 Γ— 10⁹⁷(98-digit number)
24873153233905894254…12446112525393919999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.974 Γ— 10⁹⁷(98-digit number)
49746306467811788508…24892225050787839999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
9.949 Γ— 10⁹⁷(98-digit number)
99492612935623577017…49784450101575679999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2633775

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 293dc37a2d0e537d733f5dfefa2dfc24cb96e609c76505bbe588cf10ec6edb0a

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 #2,633,775 on Chainz β†—
Circulating Supply:57,893,114 XPMΒ·at block #6,831,120 Β· updates every 60s
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