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Block #102,278

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2013, 1:32:11 AM Β· Difficulty 9.4882 Β· 6,715,696 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
499f9d2f9161d08e528c93b357573be2cfe20e18bdea4f42db3670c4ac9790a7
View on Chainz β†—

Height

#102,278

Difficulty

9.488172

Transactions

1

Size

199 B

Version

2

Bits

097cf8d1

Nonce

333,171

Timestamp

8/7/2013, 1:32:11 AM

Confirmations

6,715,696

Merkle Root

6e89e09f4c842e805fc41d95cc654e626c785e14b6da64d7beb36d05948266f5
Transactions (1)
Coinbase6e89e09f4c842e…b36d05948266f5
1 in β†’ 1 out11.0900 XPM109 B
AZEC2Zmc…LvkK7FCz
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.

3.657 Γ— 10⁹⁴(95-digit number)
36579773993866864463…90539313899103640740
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
3.657 Γ— 10⁹⁴(95-digit number)
36579773993866864463…90539313899103640741
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.315 Γ— 10⁹⁴(95-digit number)
73159547987733728926…81078627798207281481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.463 Γ— 10⁹⁡(96-digit number)
14631909597546745785…62157255596414562961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.926 Γ— 10⁹⁡(96-digit number)
29263819195093491570…24314511192829125921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.852 Γ— 10⁹⁡(96-digit number)
58527638390186983141…48629022385658251841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.170 Γ— 10⁹⁢(97-digit number)
11705527678037396628…97258044771316503681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.341 Γ— 10⁹⁢(97-digit number)
23411055356074793256…94516089542633007361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.682 Γ— 10⁹⁢(97-digit number)
46822110712149586512…89032179085266014721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.364 Γ— 10⁹⁢(97-digit number)
93644221424299173025…78064358170532029441
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 102278

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 499f9d2f9161d08e528c93b357573be2cfe20e18bdea4f42db3670c4ac9790a7

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 #102,278 on Chainz β†—
Circulating Supply:57,787,863 XPMΒ·at block #6,817,973 Β· updates every 60s
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