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Home/Chain Registry/Block #2,646,050

Block #2,646,050

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 5/3/2018, 4:30:15 AM Β· Difficulty 11.7438 Β· 4,199,599 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6c7361a8a537d3a12a17c9f4470baf5192b7f50fb9de54ab0721a52911a47de9
View on Chainz β†—

Difficulty

11.743838

Transactions

3

Size

2.26 KB

Version

2

Bits

0bbe6c32

Nonce

644,037,481

Timestamp

5/3/2018, 4:30:15 AM

Confirmations

4,199,599

Merkle Root

97b3093378afea53e2bee0a842d37d3c0d91380c3c4c035cc9f12690b03d4b2e
Transactions (3)
Coinbase6a2a4fb77d8f5a…52089ca6fda3d3
1 in β†’ 1 out7.2700 XPM110 B
Adqah8zh…1WwoHJ9t
552808d0797e06…5ac3ffee747214
2 in β†’ 3 out46.0483 XPM410 B
ANQT6hq3…SNnTb8e2AdgXxNBs…M2rqoAQnASk9H3sY…qUG8r1d4
fef8e2b1af6ddb…7ce1b5f41e8eb3
11 in β†’ 2 out100.9400 XPM1.67 KB
AS4wJ8cz…PMr3hhPvAL4Ei8E7…gmWk2UWo
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.

7.387 Γ— 10⁹⁴(95-digit number)
73875994261831320215…22774363649663768380
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
7.387 Γ— 10⁹⁴(95-digit number)
73875994261831320215…22774363649663768379
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.477 Γ— 10⁹⁡(96-digit number)
14775198852366264043…45548727299327536759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.955 Γ— 10⁹⁡(96-digit number)
29550397704732528086…91097454598655073519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.910 Γ— 10⁹⁡(96-digit number)
59100795409465056172…82194909197310147039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.182 Γ— 10⁹⁢(97-digit number)
11820159081893011234…64389818394620294079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.364 Γ— 10⁹⁢(97-digit number)
23640318163786022469…28779636789240588159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.728 Γ— 10⁹⁢(97-digit number)
47280636327572044938…57559273578481176319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.456 Γ— 10⁹⁢(97-digit number)
94561272655144089876…15118547156962352639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.891 Γ— 10⁹⁷(98-digit number)
18912254531028817975…30237094313924705279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.782 Γ— 10⁹⁷(98-digit number)
37824509062057635950…60474188627849410559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.564 Γ— 10⁹⁷(98-digit number)
75649018124115271900…20948377255698821119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.512 Γ— 10⁹⁸(99-digit number)
15129803624823054380…41896754511397642239
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 2646050

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 6c7361a8a537d3a12a17c9f4470baf5192b7f50fb9de54ab0721a52911a47de9

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 #2,646,050 on Chainz β†—
Circulating Supply:58,009,641 XPMΒ·at block #6,845,648 Β· updates every 60s
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