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Block #333,503

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/28/2013, 8:22:52 PM Β· Difficulty 10.1603 Β· 6,481,485 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bd7f57a1c12a4b6ccd122ea23e4d9dd5b91f89728caf2da69ff3d2cf92bfa372
View on Chainz β†—

Height

#333,503

Difficulty

10.160287

Transactions

1

Size

210 B

Version

2

Bits

0a29088f

Nonce

2,763

Timestamp

12/28/2013, 8:22:52 PM

Confirmations

6,481,485

Merkle Root

d4599a1d472b23f5fbe56bcc73c320b135266d3507def0a083208ed1a019dbf2
Transactions (1)
Coinbased4599a1d472b23…208ed1a019dbf2
1 in β†’ 1 out9.6700 XPM116 B
AbwWkWZt…kawDhufa
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.

1.312 Γ— 10¹⁰⁡(106-digit number)
13121305336004046143…97233398791109191680
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
1.312 Γ— 10¹⁰⁡(106-digit number)
13121305336004046143…97233398791109191679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.624 Γ— 10¹⁰⁡(106-digit number)
26242610672008092287…94466797582218383359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.248 Γ— 10¹⁰⁡(106-digit number)
52485221344016184574…88933595164436766719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.049 Γ— 10¹⁰⁢(107-digit number)
10497044268803236914…77867190328873533439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.099 Γ— 10¹⁰⁢(107-digit number)
20994088537606473829…55734380657747066879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.198 Γ— 10¹⁰⁢(107-digit number)
41988177075212947659…11468761315494133759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.397 Γ— 10¹⁰⁢(107-digit number)
83976354150425895319…22937522630988267519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.679 Γ— 10¹⁰⁷(108-digit number)
16795270830085179063…45875045261976535039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.359 Γ— 10¹⁰⁷(108-digit number)
33590541660170358127…91750090523953070079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.718 Γ— 10¹⁰⁷(108-digit number)
67181083320340716255…83500181047906140159
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 333503

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 bd7f57a1c12a4b6ccd122ea23e4d9dd5b91f89728caf2da69ff3d2cf92bfa372

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 #333,503 on Chainz β†—
Circulating Supply:57,763,989 XPMΒ·at block #6,814,987 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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