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Block #183,946

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/28/2013, 8:39:33 AM Β· Difficulty 9.8586 Β· 6,640,633 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7192542433970961d526ca8e8214affd1b4ea35e94ab46f2b3270f041d00bae6
View on Chainz β†—

Height

#183,946

Difficulty

9.858554

Transactions

1

Size

197 B

Version

2

Bits

09dbca37

Nonce

4,719

Timestamp

9/28/2013, 8:39:33 AM

Confirmations

6,640,633

Merkle Root

89d7603c1713073d0f0e1ccca5520574e364cc1bc21902b1450ad12b4ef90adc
Transactions (1)
Coinbase89d7603c171307…0ad12b4ef90adc
1 in β†’ 1 out10.2700 XPM109 B
AdeHAbFR…Jd2VNP3F
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.

2.180 Γ— 10⁹⁰(91-digit number)
21809298349897892739…48177776454214548440
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
2.180 Γ— 10⁹⁰(91-digit number)
21809298349897892739…48177776454214548439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.361 Γ— 10⁹⁰(91-digit number)
43618596699795785478…96355552908429096879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.723 Γ— 10⁹⁰(91-digit number)
87237193399591570957…92711105816858193759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.744 Γ— 10⁹¹(92-digit number)
17447438679918314191…85422211633716387519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.489 Γ— 10⁹¹(92-digit number)
34894877359836628382…70844423267432775039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.978 Γ— 10⁹¹(92-digit number)
69789754719673256765…41688846534865550079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.395 Γ— 10⁹²(93-digit number)
13957950943934651353…83377693069731100159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.791 Γ— 10⁹²(93-digit number)
27915901887869302706…66755386139462200319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.583 Γ— 10⁹²(93-digit number)
55831803775738605412…33510772278924400639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.116 Γ— 10⁹³(94-digit number)
11166360755147721082…67021544557848801279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 183946

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 7192542433970961d526ca8e8214affd1b4ea35e94ab46f2b3270f041d00bae6

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 #183,946 on Chainz β†—
Circulating Supply:57,840,699 XPMΒ·at block #6,824,578 Β· updates every 60s
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