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Block #476,134

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/5/2014, 3:37:29 PM Β· Difficulty 10.4689 Β· 6,325,731 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0768734aa8cc6e6a3a52b8395c23f2020aae9c61fe03434adf44c414f6a4b88d
View on Chainz β†—

Height

#476,134

Difficulty

10.468890

Transactions

1

Size

257 B

Version

2

Bits

0a780933

Nonce

90,351

Timestamp

4/5/2014, 3:37:29 PM

Confirmations

6,325,731

Merkle Root

2d2e3c16c25455126fe424ce38ec1da1eb39cc8fec17bea576485b7da5b07cca
Transactions (1)
Coinbase2d2e3c16c25455…485b7da5b07cca
1 in β†’ 3 out9.1100 XPM165 B
AMVf7Jrg…xd5AVR7CALzzzbUz…2Cb4jSDNAJno7LX2…vo4wdWtY
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.

3.996 Γ— 10⁹⁸(99-digit number)
39967182478557577468…22557631285594782720
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
3.996 Γ— 10⁹⁸(99-digit number)
39967182478557577468…22557631285594782719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.993 Γ— 10⁹⁸(99-digit number)
79934364957115154937…45115262571189565439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.598 Γ— 10⁹⁹(100-digit number)
15986872991423030987…90230525142379130879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.197 Γ— 10⁹⁹(100-digit number)
31973745982846061975…80461050284758261759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.394 Γ— 10⁹⁹(100-digit number)
63947491965692123950…60922100569516523519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.278 Γ— 10¹⁰⁰(101-digit number)
12789498393138424790…21844201139033047039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.557 Γ— 10¹⁰⁰(101-digit number)
25578996786276849580…43688402278066094079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.115 Γ— 10¹⁰⁰(101-digit number)
51157993572553699160…87376804556132188159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.023 Γ— 10¹⁰¹(102-digit number)
10231598714510739832…74753609112264376319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.046 Γ— 10¹⁰¹(102-digit number)
20463197429021479664…49507218224528752639
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 476134

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 0768734aa8cc6e6a3a52b8395c23f2020aae9c61fe03434adf44c414f6a4b88d

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 #476,134 on Chainz β†—
Circulating Supply:57,659,012 XPMΒ·at block #6,801,864 Β· updates every 60s
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