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Block #271,147

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/24/2013, 11:05:07 AM Β· Difficulty 9.9516 Β· 6,555,197 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5a532ca9c443cd75e9ebb67b053555c4864894006a953f9bac2908987be3b2fa
View on Chainz β†—

Height

#271,147

Difficulty

9.951567

Transactions

1

Size

207 B

Version

2

Bits

09f399eb

Nonce

234,047

Timestamp

11/24/2013, 11:05:07 AM

Confirmations

6,555,197

Merkle Root

faee89f3ffc5ce056d4bab6299ae395e58f6c7b81ebcd9e9a5801b7b814eccd1
Transactions (1)
Coinbasefaee89f3ffc5ce…801b7b814eccd1
1 in β†’ 1 out10.0800 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.230 Γ— 10⁹⁸(99-digit number)
12308255543320179611…22199566341427937280
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
1.230 Γ— 10⁹⁸(99-digit number)
12308255543320179611…22199566341427937279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.461 Γ— 10⁹⁸(99-digit number)
24616511086640359223…44399132682855874559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.923 Γ— 10⁹⁸(99-digit number)
49233022173280718446…88798265365711749119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.846 Γ— 10⁹⁸(99-digit number)
98466044346561436893…77596530731423498239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.969 Γ— 10⁹⁹(100-digit number)
19693208869312287378…55193061462846996479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.938 Γ— 10⁹⁹(100-digit number)
39386417738624574757…10386122925693992959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.877 Γ— 10⁹⁹(100-digit number)
78772835477249149514…20772245851387985919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.575 Γ— 10¹⁰⁰(101-digit number)
15754567095449829902…41544491702775971839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.150 Γ— 10¹⁰⁰(101-digit number)
31509134190899659805…83088983405551943679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.301 Γ— 10¹⁰⁰(101-digit number)
63018268381799319611…66177966811103887359
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 271147

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 5a532ca9c443cd75e9ebb67b053555c4864894006a953f9bac2908987be3b2fa

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 #271,147 on Chainz β†—
Circulating Supply:57,854,896 XPMΒ·at block #6,826,343 Β· updates every 60s
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