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Block #194,785

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/5/2013, 8:49:33 AM Β· Difficulty 9.8800 Β· 6,610,186 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f3fb5194e8a0c08ab7ba62c10d0937b023732c565bd2dcb4e120e4fc4ea34e62
View on Chainz β†—

Height

#194,785

Difficulty

9.879990

Transactions

2

Size

425 B

Version

2

Bits

09e14700

Nonce

113,062

Timestamp

10/5/2013, 8:49:33 AM

Confirmations

6,610,186

Merkle Root

26cd58b94c6c9cafa0007fb57643e80f44b3beb23ce0fbf8f7a8aac316d4af22
Transactions (2)
Coinbase13e22c15228a06…0da986edfffd77
1 in β†’ 1 out10.2400 XPM109 B
AY3Rt1ex…GJoFTK6u
5cb59f4cebd5f0…16762b4732ff16
1 in β†’ 2 out128.0521 XPM227 B
AMyK1rVd…9RBG9Tb4AbZhKgjp…oJM6h1aX
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.

3.639 Γ— 10⁹²(93-digit number)
36397996411365919595…40117943520689471040
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
3.639 Γ— 10⁹²(93-digit number)
36397996411365919595…40117943520689471039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.279 Γ— 10⁹²(93-digit number)
72795992822731839190…80235887041378942079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.455 Γ— 10⁹³(94-digit number)
14559198564546367838…60471774082757884159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.911 Γ— 10⁹³(94-digit number)
29118397129092735676…20943548165515768319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.823 Γ— 10⁹³(94-digit number)
58236794258185471352…41887096331031536639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.164 Γ— 10⁹⁴(95-digit number)
11647358851637094270…83774192662063073279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.329 Γ— 10⁹⁴(95-digit number)
23294717703274188540…67548385324126146559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.658 Γ— 10⁹⁴(95-digit number)
46589435406548377081…35096770648252293119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.317 Γ— 10⁹⁴(95-digit number)
93178870813096754163…70193541296504586239
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 194785

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 f3fb5194e8a0c08ab7ba62c10d0937b023732c565bd2dcb4e120e4fc4ea34e62

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 #194,785 on Chainz β†—
Circulating Supply:57,683,836 XPMΒ·at block #6,804,970 Β· updates every 60s
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