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Home/Chain Registry/Block #50,965

Block #50,965

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 3:46:00 AM Β· Difficulty 8.8911 Β· 6,754,659 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
99f0401a5629d488f75dc35295ec433cc479e5d2f891186472fed332ba37fbd5
View on Chainz β†—

Height

#50,965

Difficulty

8.891090

Transactions

1

Size

199 B

Version

2

Bits

08e41e7b

Nonce

802

Timestamp

7/16/2013, 3:46:00 AM

Confirmations

6,754,659

Merkle Root

964392c11564a5995c1ca62c77162510d0cd014a6333907d0852191d6dd95ee3
Transactions (1)
Coinbase964392c11564a5…52191d6dd95ee3
1 in β†’ 1 out12.6300 XPM110 B
AMJGTwKc…k18kkTir
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.

3.158 Γ— 10⁹¹(92-digit number)
31580966855504168232…23005416282635116950
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
3.158 Γ— 10⁹¹(92-digit number)
31580966855504168232…23005416282635116949
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.316 Γ— 10⁹¹(92-digit number)
63161933711008336464…46010832565270233899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.263 Γ— 10⁹²(93-digit number)
12632386742201667292…92021665130540467799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.526 Γ— 10⁹²(93-digit number)
25264773484403334585…84043330261080935599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.052 Γ— 10⁹²(93-digit number)
50529546968806669171…68086660522161871199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.010 Γ— 10⁹³(94-digit number)
10105909393761333834…36173321044323742399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.021 Γ— 10⁹³(94-digit number)
20211818787522667668…72346642088647484799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.042 Γ— 10⁹³(94-digit number)
40423637575045335337…44693284177294969599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 50965

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 99f0401a5629d488f75dc35295ec433cc479e5d2f891186472fed332ba37fbd5

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 #50,965 on Chainz β†—
Circulating Supply:57,689,066 XPMΒ·at block #6,805,623 Β· updates every 60s
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