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Block #82,777

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/25/2013, 3:55:50 PM Β· Difficulty 9.2761 Β· 6,711,743 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
49929002b98a568ed615e3a81d7c18bd8dcbf50fb489daddf533879a100fb49a
View on Chainz β†—

Height

#82,777

Difficulty

9.276102

Transactions

2

Size

388 B

Version

2

Bits

0946aea6

Nonce

4,950

Timestamp

7/25/2013, 3:55:50 PM

Confirmations

6,711,743

Merkle Root

fef23fcbce052d452cb31660cb071a5de402dfddf14a154ffc9a1176607942d9
Transactions (2)
Coinbaseb49b45d552583f…0310b6532c0d24
1 in β†’ 1 out11.6200 XPM109 B
AZsR7sxM…EQXokd43
34c1aa86a946e8…47cce89270f0c4
1 in β†’ 2 out11.6800 XPM191 B
ARh5rEeR…FG7X7G6SAa3Fe5M5…B9tp95mD
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.

2.736 Γ— 10⁹⁰(91-digit number)
27361592542141109194…24503160928880052680
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
2.736 Γ— 10⁹⁰(91-digit number)
27361592542141109194…24503160928880052679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.472 Γ— 10⁹⁰(91-digit number)
54723185084282218389…49006321857760105359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.094 Γ— 10⁹¹(92-digit number)
10944637016856443677…98012643715520210719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.188 Γ— 10⁹¹(92-digit number)
21889274033712887355…96025287431040421439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.377 Γ— 10⁹¹(92-digit number)
43778548067425774711…92050574862080842879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.755 Γ— 10⁹¹(92-digit number)
87557096134851549423…84101149724161685759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.751 Γ— 10⁹²(93-digit number)
17511419226970309884…68202299448323371519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.502 Γ— 10⁹²(93-digit number)
35022838453940619769…36404598896646743039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.004 Γ— 10⁹²(93-digit number)
70045676907881239538…72809197793293486079
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 82777

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 49929002b98a568ed615e3a81d7c18bd8dcbf50fb489daddf533879a100fb49a

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 #82,777 on Chainz β†—
Circulating Supply:57,600,198 XPMΒ·at block #6,794,519 Β· updates every 60s
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