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Block #202,671

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/10/2013, 9:15:35 AM Β· Difficulty 9.8953 Β· 6,593,146 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
19a084001a362da295916296aa330858c211a8cb50e4eb666f3be3e75cd3b71b
View on Chainz β†—

Height

#202,671

Difficulty

9.895347

Transactions

1

Size

206 B

Version

2

Bits

09e5357c

Nonce

33,555,829

Timestamp

10/10/2013, 9:15:35 AM

Confirmations

6,593,146

Merkle Root

2c6ebd93adff4a93091e8d83a7b7888797255fcdf416b52dc94c33f1c48cc82e
Transactions (1)
Coinbase2c6ebd93adff4a…4c33f1c48cc82e
1 in β†’ 1 out10.2000 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.616 Γ— 10⁹⁴(95-digit number)
16162148582547366495…89539291185068436370
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
1.616 Γ— 10⁹⁴(95-digit number)
16162148582547366495…89539291185068436371
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.232 Γ— 10⁹⁴(95-digit number)
32324297165094732990…79078582370136872741
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.464 Γ— 10⁹⁴(95-digit number)
64648594330189465980…58157164740273745481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.292 Γ— 10⁹⁡(96-digit number)
12929718866037893196…16314329480547490961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.585 Γ— 10⁹⁡(96-digit number)
25859437732075786392…32628658961094981921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.171 Γ— 10⁹⁡(96-digit number)
51718875464151572784…65257317922189963841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.034 Γ— 10⁹⁢(97-digit number)
10343775092830314556…30514635844379927681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.068 Γ— 10⁹⁢(97-digit number)
20687550185660629113…61029271688759855361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.137 Γ— 10⁹⁢(97-digit number)
41375100371321258227…22058543377519710721
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 202671

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 19a084001a362da295916296aa330858c211a8cb50e4eb666f3be3e75cd3b71b

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 #202,671 on Chainz β†—
Circulating Supply:57,610,617 XPMΒ·at block #6,795,816 Β· updates every 60s
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