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Block #275,697

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/26/2013, 8:08:27 PM Β· Difficulty 9.9614 Β· 6,550,799 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9e383bffb7124192abc64cae555b7dad1d6574fffa1b3533cbe236848c85ce40
View on Chainz β†—

Height

#275,697

Difficulty

9.961385

Transactions

2

Size

573 B

Version

2

Bits

09f61d52

Nonce

157,465

Timestamp

11/26/2013, 8:08:27 PM

Confirmations

6,550,799

Merkle Root

347e89afc4e64ab7e5509738daeab9daef2e99db58dc292e227c4fb5b0d3f723
Transactions (2)
Coinbase579486448d8c92…8e066c4a5345fe
1 in β†’ 1 out10.0700 XPM109 B
AHbLmpj3…mX4rJTua
8f5bcb1ada5bd8…fae843df62f8c7
2 in β†’ 2 out5.1166 XPM375 B
ALEBenrV…hHSTdj8oAXrmS4MX…fC8QvdLi
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.

4.222 Γ— 10⁹²(93-digit number)
42225203462646136498…57403064171260191200
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
4.222 Γ— 10⁹²(93-digit number)
42225203462646136498…57403064171260191199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.445 Γ— 10⁹²(93-digit number)
84450406925292272996…14806128342520382399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.689 Γ— 10⁹³(94-digit number)
16890081385058454599…29612256685040764799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.378 Γ— 10⁹³(94-digit number)
33780162770116909198…59224513370081529599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.756 Γ— 10⁹³(94-digit number)
67560325540233818397…18449026740163059199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.351 Γ— 10⁹⁴(95-digit number)
13512065108046763679…36898053480326118399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.702 Γ— 10⁹⁴(95-digit number)
27024130216093527358…73796106960652236799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.404 Γ— 10⁹⁴(95-digit number)
54048260432187054717…47592213921304473599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.080 Γ— 10⁹⁡(96-digit number)
10809652086437410943…95184427842608947199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.161 Γ— 10⁹⁡(96-digit number)
21619304172874821887…90368855685217894399
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 275697

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 9e383bffb7124192abc64cae555b7dad1d6574fffa1b3533cbe236848c85ce40

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 #275,697 on Chainz β†—
Circulating Supply:57,856,109 XPMΒ·at block #6,826,495 Β· updates every 60s
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