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Home/Chain Registry/Block #474,736

Block #474,736

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/4/2014, 6:21:21 PM Β· Difficulty 10.4558 Β· 6,364,013 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c051edc8dc488c199b524d5c9faa4e32a28cedb107375107d203264ce0614475
View on Chainz β†—

Height

#474,736

Difficulty

10.455797

Transactions

1

Size

202 B

Version

2

Bits

0a74af15

Nonce

493,701

Timestamp

4/4/2014, 6:21:21 PM

Confirmations

6,364,013

Merkle Root

758f5eb224414f2d87eef48c48291b86bca8043cc0dd692d89077b9562ac330b
Transactions (1)
Coinbase758f5eb224414f…077b9562ac330b
1 in β†’ 1 out9.1300 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.

8.903 Γ— 10⁹⁸(99-digit number)
89030688033411436765…00462835261588069600
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
8.903 Γ— 10⁹⁸(99-digit number)
89030688033411436765…00462835261588069601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.780 Γ— 10⁹⁹(100-digit number)
17806137606682287353…00925670523176139201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.561 Γ— 10⁹⁹(100-digit number)
35612275213364574706…01851341046352278401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.122 Γ— 10⁹⁹(100-digit number)
71224550426729149412…03702682092704556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.424 Γ— 10¹⁰⁰(101-digit number)
14244910085345829882…07405364185409113601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.848 Γ— 10¹⁰⁰(101-digit number)
28489820170691659765…14810728370818227201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.697 Γ— 10¹⁰⁰(101-digit number)
56979640341383319530…29621456741636454401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.139 Γ— 10¹⁰¹(102-digit number)
11395928068276663906…59242913483272908801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.279 Γ— 10¹⁰¹(102-digit number)
22791856136553327812…18485826966545817601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.558 Γ— 10¹⁰¹(102-digit number)
45583712273106655624…36971653933091635201
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 474736

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 c051edc8dc488c199b524d5c9faa4e32a28cedb107375107d203264ce0614475

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 #474,736 on Chainz β†—
Circulating Supply:57,954,250 XPMΒ·at block #6,838,748 Β· updates every 60s
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