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Block #196,640

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/6/2013, 3:17:10 PM Β· Difficulty 9.8809 Β· 6,615,611 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
996b5cea90b245f81a022f878251382446fe8c0471d5c2d4d7c87edb404f0de4
View on Chainz β†—

Height

#196,640

Difficulty

9.880910

Transactions

1

Size

198 B

Version

2

Bits

09e1834f

Nonce

995

Timestamp

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

Confirmations

6,615,611

Merkle Root

4ce3cab2eadb37e091b9800ef13e1c87935780c53434d60fe3127c7f57f74622
Transactions (1)
Coinbase4ce3cab2eadb37…127c7f57f74622
1 in β†’ 1 out10.2300 XPM109 B
AHefdDyT…GtGGLmzK
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.

7.590 Γ— 10⁹¹(92-digit number)
75906606668776699805…66823811764239068160
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
7.590 Γ— 10⁹¹(92-digit number)
75906606668776699805…66823811764239068159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.518 Γ— 10⁹²(93-digit number)
15181321333755339961…33647623528478136319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.036 Γ— 10⁹²(93-digit number)
30362642667510679922…67295247056956272639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.072 Γ— 10⁹²(93-digit number)
60725285335021359844…34590494113912545279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.214 Γ— 10⁹³(94-digit number)
12145057067004271968…69180988227825090559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.429 Γ— 10⁹³(94-digit number)
24290114134008543937…38361976455650181119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.858 Γ— 10⁹³(94-digit number)
48580228268017087875…76723952911300362239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.716 Γ— 10⁹³(94-digit number)
97160456536034175751…53447905822600724479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.943 Γ— 10⁹⁴(95-digit number)
19432091307206835150…06895811645201448959
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 196640

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 996b5cea90b245f81a022f878251382446fe8c0471d5c2d4d7c87edb404f0de4

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 #196,640 on Chainz β†—
Circulating Supply:57,742,025 XPMΒ·at block #6,812,250 Β· updates every 60s
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