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Home/Chain Registry/Block #337,890

Block #337,890

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/1/2014, 12:52:25 AM Β· Difficulty 10.1278 Β· 6,461,409 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e1ec935fa7044279972b9816abb346e3308a04c3c24bd55a82af0a9de4bac8d7
View on Chainz β†—

Height

#337,890

Difficulty

10.127816

Transactions

1

Size

202 B

Version

2

Bits

0a20b88b

Nonce

1,402,039

Timestamp

1/1/2014, 12:52:25 AM

Confirmations

6,461,409

Merkle Root

d343c6d692a6284adbe059de9e7f036c8f6cb185f826a365863040fd1ae0b444
Transactions (1)
Coinbased343c6d692a628…3040fd1ae0b444
1 in β†’ 1 out9.7300 XPM110 B
AeKNrjNj…1NEq95Ta
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.

7.909 Γ— 10⁹⁸(99-digit number)
79098670744746475503…42698482123735408640
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
7.909 Γ— 10⁹⁸(99-digit number)
79098670744746475503…42698482123735408639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.581 Γ— 10⁹⁹(100-digit number)
15819734148949295100…85396964247470817279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.163 Γ— 10⁹⁹(100-digit number)
31639468297898590201…70793928494941634559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.327 Γ— 10⁹⁹(100-digit number)
63278936595797180402…41587856989883269119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.265 Γ— 10¹⁰⁰(101-digit number)
12655787319159436080…83175713979766538239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.531 Γ— 10¹⁰⁰(101-digit number)
25311574638318872161…66351427959533076479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.062 Γ— 10¹⁰⁰(101-digit number)
50623149276637744322…32702855919066152959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.012 Γ— 10¹⁰¹(102-digit number)
10124629855327548864…65405711838132305919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.024 Γ— 10¹⁰¹(102-digit number)
20249259710655097728…30811423676264611839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.049 Γ— 10¹⁰¹(102-digit number)
40498519421310195457…61622847352529223679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 337890

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 e1ec935fa7044279972b9816abb346e3308a04c3c24bd55a82af0a9de4bac8d7

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 #337,890 on Chainz β†—
Circulating Supply:57,638,436 XPMΒ·at block #6,799,298 Β· updates every 60s
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