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Block #101,863

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/6/2013, 8:36:23 PM Β· Difficulty 9.4753 Β· 6,699,103 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3b4f4d4d3eff0dac36a7c8fcfab645773febbc19645e73823531b22f5e67b53f
View on Chainz β†—

Height

#101,863

Difficulty

9.475254

Transactions

1

Size

199 B

Version

2

Bits

0979aa38

Nonce

93,274

Timestamp

8/6/2013, 8:36:23 PM

Confirmations

6,699,103

Merkle Root

9ef1aae5e1658d15e363658c6c2bd2ff04978947652b1bc0631ac985907f5cc7
Transactions (1)
Coinbase9ef1aae5e1658d…1ac985907f5cc7
1 in β†’ 1 out11.1200 XPM109 B
AbB3aifu…wrbJL6FT
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.

4.388 Γ— 10⁹⁴(95-digit number)
43888488715719224538…79990076178828036020
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
4.388 Γ— 10⁹⁴(95-digit number)
43888488715719224538…79990076178828036021
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.777 Γ— 10⁹⁴(95-digit number)
87776977431438449076…59980152357656072041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.755 Γ— 10⁹⁡(96-digit number)
17555395486287689815…19960304715312144081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.511 Γ— 10⁹⁡(96-digit number)
35110790972575379630…39920609430624288161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.022 Γ— 10⁹⁡(96-digit number)
70221581945150759261…79841218861248576321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.404 Γ— 10⁹⁢(97-digit number)
14044316389030151852…59682437722497152641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.808 Γ— 10⁹⁢(97-digit number)
28088632778060303704…19364875444994305281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.617 Γ— 10⁹⁢(97-digit number)
56177265556120607409…38729750889988610561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.123 Γ— 10⁹⁷(98-digit number)
11235453111224121481…77459501779977221121
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 101863

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 3b4f4d4d3eff0dac36a7c8fcfab645773febbc19645e73823531b22f5e67b53f

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 #101,863 on Chainz β†—
Circulating Supply:57,651,786 XPMΒ·at block #6,800,965 Β· updates every 60s
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