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Block #82,775

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/25/2013, 3:53:55 PM Β· Difficulty 9.2761 Β· 6,715,839 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ae1c58ea394b7c2387e096cfc9806d46501de52d83d5ed6538e47a7038e215a8
View on Chainz β†—

Height

#82,775

Difficulty

9.276064

Transactions

1

Size

204 B

Version

2

Bits

0946ac22

Nonce

62,188

Timestamp

7/25/2013, 3:53:55 PM

Confirmations

6,715,839

Merkle Root

86ef34c3ec67258a446642261e76e9309c87fcabc9e3df700d04d58a2823eba5
Transactions (1)
Coinbase86ef34c3ec6725…04d58a2823eba5
1 in β†’ 1 out11.6100 XPM109 B
AMT2pgVo…gYkfhefu
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.

5.923 Γ— 10¹⁰⁢(107-digit number)
59231197892746124652…30346296150264679900
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
5.923 Γ— 10¹⁰⁢(107-digit number)
59231197892746124652…30346296150264679899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.184 Γ— 10¹⁰⁷(108-digit number)
11846239578549224930…60692592300529359799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.369 Γ— 10¹⁰⁷(108-digit number)
23692479157098449861…21385184601058719599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.738 Γ— 10¹⁰⁷(108-digit number)
47384958314196899722…42770369202117439199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.476 Γ— 10¹⁰⁷(108-digit number)
94769916628393799444…85540738404234878399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.895 Γ— 10¹⁰⁸(109-digit number)
18953983325678759888…71081476808469756799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.790 Γ— 10¹⁰⁸(109-digit number)
37907966651357519777…42162953616939513599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.581 Γ— 10¹⁰⁸(109-digit number)
75815933302715039555…84325907233879027199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.516 Γ— 10¹⁰⁹(110-digit number)
15163186660543007911…68651814467758054399
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 82775

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 ae1c58ea394b7c2387e096cfc9806d46501de52d83d5ed6538e47a7038e215a8

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 #82,775 on Chainz β†—
Circulating Supply:57,632,929 XPMΒ·at block #6,798,613 Β· updates every 60s
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