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Block #102,424

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2013, 3:10:29 AM Β· Difficulty 9.4930 Β· 6,696,503 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
76dade4bfa8b15811e3d45ebeab0d35f981c399d009dabcf1adb04e60da7860c
View on Chainz β†—

Height

#102,424

Difficulty

9.492967

Transactions

1

Size

199 B

Version

2

Bits

097e331a

Nonce

85,812

Timestamp

8/7/2013, 3:10:29 AM

Confirmations

6,696,503

Merkle Root

43e0d9d27ae7d705de7f86229aabaa8028bee6a6d953013681e165bfb3cb4788
Transactions (1)
Coinbase43e0d9d27ae7d7…e165bfb3cb4788
1 in β†’ 1 out11.0800 XPM109 B
AVez4Sqq…YVd2CyRi
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.

1.935 Γ— 10⁹⁡(96-digit number)
19354219719779456850…97505314695998791800
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
1.935 Γ— 10⁹⁡(96-digit number)
19354219719779456850…97505314695998791801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.870 Γ— 10⁹⁡(96-digit number)
38708439439558913701…95010629391997583601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.741 Γ— 10⁹⁡(96-digit number)
77416878879117827402…90021258783995167201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.548 Γ— 10⁹⁢(97-digit number)
15483375775823565480…80042517567990334401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.096 Γ— 10⁹⁢(97-digit number)
30966751551647130961…60085035135980668801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.193 Γ— 10⁹⁢(97-digit number)
61933503103294261922…20170070271961337601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.238 Γ— 10⁹⁷(98-digit number)
12386700620658852384…40340140543922675201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.477 Γ— 10⁹⁷(98-digit number)
24773401241317704768…80680281087845350401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.954 Γ— 10⁹⁷(98-digit number)
49546802482635409537…61360562175690700801
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 102424

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 76dade4bfa8b15811e3d45ebeab0d35f981c399d009dabcf1adb04e60da7860c

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 #102,424 on Chainz β†—
Circulating Supply:57,635,450 XPMΒ·at block #6,798,926 Β· updates every 60s
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