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Block #2,740,553

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/9/2018, 5:04:03 AM Β· Difficulty 11.6220 Β· 4,103,249 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
98e911b50b4c2ea429d0c978a189890107dfc7adfaae57ae52e9fa7a5fbc5678
View on Chainz β†—

Difficulty

11.622001

Transactions

1

Size

200 B

Version

2

Bits

0b9f3b6f

Nonce

817,629,483

Timestamp

7/9/2018, 5:04:03 AM

Confirmations

4,103,249

Merkle Root

3020d7527a0be0143309d255bc860a35c561bda5343c13cd050e92f7a0bb0c5a
Transactions (1)
Coinbase3020d7527a0be0…0e92f7a0bb0c5a
1 in β†’ 1 out7.3900 XPM110 B
AGZFvcgd…bTH67ch9
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.

4.664 Γ— 10⁹⁡(96-digit number)
46647372280757708852…05965862595236302080
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
4.664 Γ— 10⁹⁡(96-digit number)
46647372280757708852…05965862595236302079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.329 Γ— 10⁹⁡(96-digit number)
93294744561515417705…11931725190472604159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.865 Γ— 10⁹⁢(97-digit number)
18658948912303083541…23863450380945208319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.731 Γ— 10⁹⁢(97-digit number)
37317897824606167082…47726900761890416639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.463 Γ— 10⁹⁢(97-digit number)
74635795649212334164…95453801523780833279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.492 Γ— 10⁹⁷(98-digit number)
14927159129842466832…90907603047561666559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.985 Γ— 10⁹⁷(98-digit number)
29854318259684933665…81815206095123333119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.970 Γ— 10⁹⁷(98-digit number)
59708636519369867331…63630412190246666239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.194 Γ— 10⁹⁸(99-digit number)
11941727303873973466…27260824380493332479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.388 Γ— 10⁹⁸(99-digit number)
23883454607747946932…54521648760986664959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.776 Γ— 10⁹⁸(99-digit number)
47766909215495893865…09043297521973329919
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 2740553

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 98e911b50b4c2ea429d0c978a189890107dfc7adfaae57ae52e9fa7a5fbc5678

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 #2,740,553 on Chainz β†—
Circulating Supply:57,994,793 XPMΒ·at block #6,843,801 Β· updates every 60s
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