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Block #474,755

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/4/2014, 6:34:58 PM Β· Difficulty 10.4562 Β· 6,364,295 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
faa4a0cd6b7702d55dde9e624c2bc65b698ba7dc47a9896deacc9fa8618f87f1
View on Chainz β†—

Height

#474,755

Difficulty

10.456244

Transactions

1

Size

200 B

Version

2

Bits

0a74cc69

Nonce

18,997,743

Timestamp

4/4/2014, 6:34:58 PM

Confirmations

6,364,295

Merkle Root

9b7707c022d41ecac2bd404fcd136d89056743e3a4ade370e2867ae2e0415d60
Transactions (1)
Coinbase9b7707c022d41e…867ae2e0415d60
1 in β†’ 1 out9.1300 XPM109 B
AY3iAsmW…kTp2yT2W
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.

3.490 Γ— 10⁹⁢(97-digit number)
34900523680930274384…38303837837354818560
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
3.490 Γ— 10⁹⁢(97-digit number)
34900523680930274384…38303837837354818559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.980 Γ— 10⁹⁢(97-digit number)
69801047361860548769…76607675674709637119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.396 Γ— 10⁹⁷(98-digit number)
13960209472372109753…53215351349419274239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.792 Γ— 10⁹⁷(98-digit number)
27920418944744219507…06430702698838548479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.584 Γ— 10⁹⁷(98-digit number)
55840837889488439015…12861405397677096959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.116 Γ— 10⁹⁸(99-digit number)
11168167577897687803…25722810795354193919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.233 Γ— 10⁹⁸(99-digit number)
22336335155795375606…51445621590708387839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.467 Γ— 10⁹⁸(99-digit number)
44672670311590751212…02891243181416775679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.934 Γ— 10⁹⁸(99-digit number)
89345340623181502424…05782486362833551359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.786 Γ— 10⁹⁹(100-digit number)
17869068124636300484…11564972725667102719
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 474755

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 faa4a0cd6b7702d55dde9e624c2bc65b698ba7dc47a9896deacc9fa8618f87f1

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 #474,755 on Chainz β†—
Circulating Supply:57,956,670 XPMΒ·at block #6,839,049 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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