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Home/Chain Registry/Block #334,936

Block #334,936

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/29/2013, 8:18:40 PM Β· Difficulty 10.1605 Β· 6,481,652 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7ac0cd29ea424cc950a62701fdba729ee1dadebdfb94ed95fa927aa5f1153bfa
View on Chainz β†—

Height

#334,936

Difficulty

10.160524

Transactions

1

Size

200 B

Version

2

Bits

0a29181e

Nonce

102,468

Timestamp

12/29/2013, 8:18:40 PM

Confirmations

6,481,652

Merkle Root

70bb100582c83d2e39d7f33b43dae3449fd17ab89f45b89bd950e92aa5a9dd4c
Transactions (1)
Coinbase70bb100582c83d…50e92aa5a9dd4c
1 in β†’ 1 out9.6700 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.

1.496 Γ— 10⁹⁴(95-digit number)
14962469739849386137…17512696175372702080
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
1.496 Γ— 10⁹⁴(95-digit number)
14962469739849386137…17512696175372702079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.992 Γ— 10⁹⁴(95-digit number)
29924939479698772275…35025392350745404159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.984 Γ— 10⁹⁴(95-digit number)
59849878959397544550…70050784701490808319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.196 Γ— 10⁹⁡(96-digit number)
11969975791879508910…40101569402981616639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.393 Γ— 10⁹⁡(96-digit number)
23939951583759017820…80203138805963233279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.787 Γ— 10⁹⁡(96-digit number)
47879903167518035640…60406277611926466559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.575 Γ— 10⁹⁡(96-digit number)
95759806335036071280…20812555223852933119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.915 Γ— 10⁹⁢(97-digit number)
19151961267007214256…41625110447705866239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.830 Γ— 10⁹⁢(97-digit number)
38303922534014428512…83250220895411732479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.660 Γ— 10⁹⁢(97-digit number)
76607845068028857024…66500441790823464959
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 334936

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 7ac0cd29ea424cc950a62701fdba729ee1dadebdfb94ed95fa927aa5f1153bfa

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 #334,936 on Chainz β†—
Circulating Supply:57,776,827 XPMΒ·at block #6,816,587 Β· updates every 60s
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