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Block #478,283

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/6/2014, 11:46:44 PM Β· Difficulty 10.4919 Β· 6,348,860 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cf8acf5fdb50e36141c258300e2b445af4b6d207eaf2d709b5d7061749e84ce5
View on Chainz β†—

Height

#478,283

Difficulty

10.491910

Transactions

1

Size

207 B

Version

2

Bits

0a7dedd3

Nonce

24,414

Timestamp

4/6/2014, 11:46:44 PM

Confirmations

6,348,860

Merkle Root

9d7ed94f01d2ed910f83cf617a06720bef529995b316fcda4ef099138c542baa
Transactions (1)
Coinbase9d7ed94f01d2ed…f099138c542baa
1 in β†’ 1 out9.0700 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.

5.174 Γ— 10⁹⁷(98-digit number)
51747283749991084727…74242930403114806400
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
5.174 Γ— 10⁹⁷(98-digit number)
51747283749991084727…74242930403114806399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.034 Γ— 10⁹⁸(99-digit number)
10349456749998216945…48485860806229612799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.069 Γ— 10⁹⁸(99-digit number)
20698913499996433891…96971721612459225599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.139 Γ— 10⁹⁸(99-digit number)
41397826999992867782…93943443224918451199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.279 Γ— 10⁹⁸(99-digit number)
82795653999985735564…87886886449836902399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.655 Γ— 10⁹⁹(100-digit number)
16559130799997147112…75773772899673804799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.311 Γ— 10⁹⁹(100-digit number)
33118261599994294225…51547545799347609599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.623 Γ— 10⁹⁹(100-digit number)
66236523199988588451…03095091598695219199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.324 Γ— 10¹⁰⁰(101-digit number)
13247304639997717690…06190183197390438399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.649 Γ— 10¹⁰⁰(101-digit number)
26494609279995435380…12380366394780876799
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 478283

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 cf8acf5fdb50e36141c258300e2b445af4b6d207eaf2d709b5d7061749e84ce5

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 #478,283 on Chainz β†—
Circulating Supply:57,861,326 XPMΒ·at block #6,827,142 Β· updates every 60s
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