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Home/Chain Registry/Block #2,739,553

Block #2,739,553

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/8/2018, 1:00:08 PM Β· Difficulty 11.6193 Β· 4,102,037 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
20080b2c6291dda2e83684925497cb8c17296b26f3e638b4968e12feedf84e7d
View on Chainz β†—

Difficulty

11.619297

Transactions

2

Size

722 B

Version

2

Bits

0b9e8a3a

Nonce

256,256,118

Timestamp

7/8/2018, 1:00:08 PM

Confirmations

4,102,037

Merkle Root

8fd914d9277c3ffeec249c0e067a348b72a0f60b278c54082ab78fb29a81ce09
Transactions (2)
Coinbasebe72a34c88cd97…f91ba0507ad93d
1 in β†’ 1 out7.4000 XPM110 B
AProgBzn…yY9zVCXi
13bc386ac14539…fc68df40e5e183
3 in β†’ 2 out98.0099 XPM523 B
ARY67Yio…VS88Q8ouAYexAfT9…ZyK7bwZR
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.

2.327 Γ— 10⁹²(93-digit number)
23277181993897929058…20286854649367350500
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
2.327 Γ— 10⁹²(93-digit number)
23277181993897929058…20286854649367350499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.655 Γ— 10⁹²(93-digit number)
46554363987795858117…40573709298734700999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.310 Γ— 10⁹²(93-digit number)
93108727975591716235…81147418597469401999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.862 Γ— 10⁹³(94-digit number)
18621745595118343247…62294837194938803999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.724 Γ— 10⁹³(94-digit number)
37243491190236686494…24589674389877607999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.448 Γ— 10⁹³(94-digit number)
74486982380473372988…49179348779755215999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.489 Γ— 10⁹⁴(95-digit number)
14897396476094674597…98358697559510431999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.979 Γ— 10⁹⁴(95-digit number)
29794792952189349195…96717395119020863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.958 Γ— 10⁹⁴(95-digit number)
59589585904378698390…93434790238041727999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.191 Γ— 10⁹⁡(96-digit number)
11917917180875739678…86869580476083455999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.383 Γ— 10⁹⁡(96-digit number)
23835834361751479356…73739160952166911999
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 2739553

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 20080b2c6291dda2e83684925497cb8c17296b26f3e638b4968e12feedf84e7d

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 #2,739,553 on Chainz β†—
Circulating Supply:57,977,107 XPMΒ·at block #6,841,589 Β· updates every 60s
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