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Block #337,825

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/31/2013, 11:39:16 PM Β· Difficulty 10.1293 Β· 6,463,677 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e5a5a2636057b18d8b343703594c1b68d7d463abe5f2a6bc2bd888e45f336ae7
View on Chainz β†—

Height

#337,825

Difficulty

10.129323

Transactions

1

Size

201 B

Version

2

Bits

0a211b50

Nonce

256,906

Timestamp

12/31/2013, 11:39:16 PM

Confirmations

6,463,677

Merkle Root

273120f599b52a87870b6321e24daa15329c673ce0328d217898caae7e7876d8
Transactions (1)
Coinbase273120f599b52a…98caae7e7876d8
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.

1.518 Γ— 10⁹⁸(99-digit number)
15186276013197878346…43982619178673375680
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
1.518 Γ— 10⁹⁸(99-digit number)
15186276013197878346…43982619178673375679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.037 Γ— 10⁹⁸(99-digit number)
30372552026395756693…87965238357346751359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.074 Γ— 10⁹⁸(99-digit number)
60745104052791513387…75930476714693502719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.214 Γ— 10⁹⁹(100-digit number)
12149020810558302677…51860953429387005439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.429 Γ— 10⁹⁹(100-digit number)
24298041621116605354…03721906858774010879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.859 Γ— 10⁹⁹(100-digit number)
48596083242233210709…07443813717548021759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.719 Γ— 10⁹⁹(100-digit number)
97192166484466421419…14887627435096043519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.943 Γ— 10¹⁰⁰(101-digit number)
19438433296893284283…29775254870192087039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.887 Γ— 10¹⁰⁰(101-digit number)
38876866593786568567…59550509740384174079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.775 Γ— 10¹⁰⁰(101-digit number)
77753733187573137135…19101019480768348159
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 337825

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 e5a5a2636057b18d8b343703594c1b68d7d463abe5f2a6bc2bd888e45f336ae7

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 #337,825 on Chainz β†—
Circulating Supply:57,656,089 XPMΒ·at block #6,801,501 Β· updates every 60s
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