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Block #82,888

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/25/2013, 6:09:34 PM Β· Difficulty 9.2729 Β· 6,719,344 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c67b20bdd6111a312fe839bf76ca7524f250c4f80ce60958f5aa2f80ceb32d2e
View on Chainz β†—

Height

#82,888

Difficulty

9.272868

Transactions

1

Size

200 B

Version

2

Bits

0945dab3

Nonce

114,811

Timestamp

7/25/2013, 6:09:34 PM

Confirmations

6,719,344

Merkle Root

51bca503a52b3c09df7480ec93a0541542cc250e4abe25b326fee0e7097538d4
Transactions (1)
Coinbase51bca503a52b3c…fee0e7097538d4
1 in β†’ 1 out11.6100 XPM109 B
ATBY7248…NexmBqqT
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.

2.467 Γ— 10⁹⁢(97-digit number)
24670784760429647885…97474724064041694080
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
2.467 Γ— 10⁹⁢(97-digit number)
24670784760429647885…97474724064041694079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.934 Γ— 10⁹⁢(97-digit number)
49341569520859295771…94949448128083388159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.868 Γ— 10⁹⁢(97-digit number)
98683139041718591543…89898896256166776319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.973 Γ— 10⁹⁷(98-digit number)
19736627808343718308…79797792512333552639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.947 Γ— 10⁹⁷(98-digit number)
39473255616687436617…59595585024667105279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.894 Γ— 10⁹⁷(98-digit number)
78946511233374873235…19191170049334210559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.578 Γ— 10⁹⁸(99-digit number)
15789302246674974647…38382340098668421119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.157 Γ— 10⁹⁸(99-digit number)
31578604493349949294…76764680197336842239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.315 Γ— 10⁹⁸(99-digit number)
63157208986699898588…53529360394673684479
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 82888

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 c67b20bdd6111a312fe839bf76ca7524f250c4f80ce60958f5aa2f80ceb32d2e

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 #82,888 on Chainz β†—
Circulating Supply:57,661,864 XPMΒ·at block #6,802,231 Β· updates every 60s
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