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Block #277,612

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/27/2013, 3:40:20 PM Β· Difficulty 9.9667 Β· 6,523,838 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
eefc745a68a28e38ccc3bdab493a8a3f39f60e69234a024e9f064e1c30feacd2
View on Chainz β†—

Height

#277,612

Difficulty

9.966744

Transactions

1

Size

201 B

Version

2

Bits

09f77c90

Nonce

8,492

Timestamp

11/27/2013, 3:40:20 PM

Confirmations

6,523,838

Merkle Root

037a727def2a0b93e0024fcd95ef89a21b81f9b07784040b71dd577cdccb3239
Transactions (1)
Coinbase037a727def2a0b…dd577cdccb3239
1 in β†’ 1 out10.0500 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.

1.943 Γ— 10⁹⁸(99-digit number)
19437429645527362591…89757336647487084100
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
1.943 Γ— 10⁹⁸(99-digit number)
19437429645527362591…89757336647487084099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.887 Γ— 10⁹⁸(99-digit number)
38874859291054725183…79514673294974168199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.774 Γ— 10⁹⁸(99-digit number)
77749718582109450367…59029346589948336399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.554 Γ— 10⁹⁹(100-digit number)
15549943716421890073…18058693179896672799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.109 Γ— 10⁹⁹(100-digit number)
31099887432843780147…36117386359793345599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.219 Γ— 10⁹⁹(100-digit number)
62199774865687560294…72234772719586691199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.243 Γ— 10¹⁰⁰(101-digit number)
12439954973137512058…44469545439173382399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.487 Γ— 10¹⁰⁰(101-digit number)
24879909946275024117…88939090878346764799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.975 Γ— 10¹⁰⁰(101-digit number)
49759819892550048235…77878181756693529599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.951 Γ— 10¹⁰⁰(101-digit number)
99519639785100096470…55756363513387059199
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 277612

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 eefc745a68a28e38ccc3bdab493a8a3f39f60e69234a024e9f064e1c30feacd2

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 #277,612 on Chainz β†—
Circulating Supply:57,655,673 XPMΒ·at block #6,801,449 Β· updates every 60s
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