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Home/Chain Registry/Block #2,752,292

Block #2,752,292

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2018, 2:39:36 AM Β· Difficulty 11.6487 Β· 4,091,677 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
63a082f25b27d2fbfc92e5bd8360816c66ba7f83d16577f8be8f5bf164affe16
View on Chainz β†—

Difficulty

11.648683

Transactions

1

Size

199 B

Version

2

Bits

0ba6100f

Nonce

67,929,761

Timestamp

7/17/2018, 2:39:36 AM

Confirmations

4,091,677

Merkle Root

fdf251d5044fda352591b47dad8e66b8a2d10bdec47ba0559ecb88846b6e4625
Transactions (1)
Coinbasefdf251d5044fda…cb88846b6e4625
1 in β†’ 1 out7.3600 XPM109 B
AZtxQr2F…7grUWrUz
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.

3.027 Γ— 10⁹⁡(96-digit number)
30271470270111177070…21595416576442977280
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
3.027 Γ— 10⁹⁡(96-digit number)
30271470270111177070…21595416576442977281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.054 Γ— 10⁹⁡(96-digit number)
60542940540222354140…43190833152885954561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.210 Γ— 10⁹⁢(97-digit number)
12108588108044470828…86381666305771909121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.421 Γ— 10⁹⁢(97-digit number)
24217176216088941656…72763332611543818241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.843 Γ— 10⁹⁢(97-digit number)
48434352432177883312…45526665223087636481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.686 Γ— 10⁹⁢(97-digit number)
96868704864355766625…91053330446175272961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.937 Γ— 10⁹⁷(98-digit number)
19373740972871153325…82106660892350545921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.874 Γ— 10⁹⁷(98-digit number)
38747481945742306650…64213321784701091841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.749 Γ— 10⁹⁷(98-digit number)
77494963891484613300…28426643569402183681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.549 Γ— 10⁹⁸(99-digit number)
15498992778296922660…56853287138804367361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.099 Γ— 10⁹⁸(99-digit number)
30997985556593845320…13706574277608734721
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2752292

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 63a082f25b27d2fbfc92e5bd8360816c66ba7f83d16577f8be8f5bf164affe16

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 #2,752,292 on Chainz β†—
Circulating Supply:57,996,130 XPMΒ·at block #6,843,968 Β· updates every 60s
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