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Home/Chain Registry/Block #2,648,317

Block #2,648,317

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 10:42:59 AM Β· Difficulty 11.7660 Β· 4,194,569 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9b59e14dad3817f2e84e7e6e91f8697d57b4a67f3b06e87f6e8ac926357167e8
View on Chainz β†—

Difficulty

11.765953

Transactions

1

Size

201 B

Version

2

Bits

0bc4157b

Nonce

353,944,340

Timestamp

5/4/2018, 10:42:59 AM

Confirmations

4,194,569

Merkle Root

e5672b2c7bba331c6afa22b5233c93f40dbceefefec332e6a72c2211b78bc7b5
Transactions (1)
Coinbasee5672b2c7bba33…2c2211b78bc7b5
1 in β†’ 1 out7.2100 XPM110 B
AQstXLiR…yN8MsKye
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.

5.619 Γ— 10⁹⁷(98-digit number)
56198010737962756288…01596910750657617920
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
5.619 Γ— 10⁹⁷(98-digit number)
56198010737962756288…01596910750657617919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.123 Γ— 10⁹⁸(99-digit number)
11239602147592551257…03193821501315235839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.247 Γ— 10⁹⁸(99-digit number)
22479204295185102515…06387643002630471679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.495 Γ— 10⁹⁸(99-digit number)
44958408590370205030…12775286005260943359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.991 Γ— 10⁹⁸(99-digit number)
89916817180740410061…25550572010521886719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.798 Γ— 10⁹⁹(100-digit number)
17983363436148082012…51101144021043773439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.596 Γ— 10⁹⁹(100-digit number)
35966726872296164024…02202288042087546879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.193 Γ— 10⁹⁹(100-digit number)
71933453744592328049…04404576084175093759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.438 Γ— 10¹⁰⁰(101-digit number)
14386690748918465609…08809152168350187519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.877 Γ— 10¹⁰⁰(101-digit number)
28773381497836931219…17618304336700375039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.754 Γ— 10¹⁰⁰(101-digit number)
57546762995673862439…35236608673400750079
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 2648317

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 9b59e14dad3817f2e84e7e6e91f8697d57b4a67f3b06e87f6e8ac926357167e8

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 #2,648,317 on Chainz β†—
Circulating Supply:57,987,434 XPMΒ·at block #6,842,885 Β· updates every 60s
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