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Block #196,639

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/6/2013, 3:17:07 PM Β· Difficulty 9.8809 Β· 6,615,037 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8c253546d2587481451880388ced6c7136819358772f0756c15a0ec15a7d6312
View on Chainz β†—

Height

#196,639

Difficulty

9.880893

Transactions

1

Size

199 B

Version

2

Bits

09e18239

Nonce

58,844

Timestamp

10/6/2013, 3:17:07 PM

Confirmations

6,615,037

Merkle Root

5adf578ee1e23c321a51e0dc07be7cb15e6fd2457a0e1c6fea46bde44a8387a7
Transactions (1)
Coinbase5adf578ee1e23c…46bde44a8387a7
1 in β†’ 1 out10.2300 XPM109 B
AK7kWkL4…GHfWFBHC
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.

1.757 Γ— 10⁹⁴(95-digit number)
17576491325571581696…41191234044961667600
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
1.757 Γ— 10⁹⁴(95-digit number)
17576491325571581696…41191234044961667601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.515 Γ— 10⁹⁴(95-digit number)
35152982651143163392…82382468089923335201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.030 Γ— 10⁹⁴(95-digit number)
70305965302286326785…64764936179846670401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.406 Γ— 10⁹⁡(96-digit number)
14061193060457265357…29529872359693340801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.812 Γ— 10⁹⁡(96-digit number)
28122386120914530714…59059744719386681601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.624 Γ— 10⁹⁡(96-digit number)
56244772241829061428…18119489438773363201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.124 Γ— 10⁹⁢(97-digit number)
11248954448365812285…36238978877546726401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.249 Γ— 10⁹⁢(97-digit number)
22497908896731624571…72477957755093452801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.499 Γ— 10⁹⁢(97-digit number)
44995817793463249143…44955915510186905601
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 196639

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 8c253546d2587481451880388ced6c7136819358772f0756c15a0ec15a7d6312

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 #196,639 on Chainz β†—
Circulating Supply:57,737,515 XPMΒ·at block #6,811,675 Β· updates every 60s
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