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Block #87,118

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/28/2013, 3:44:36 PM Β· Difficulty 9.2809 Β· 6,713,149 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7b1e30486b10855922e26dde510db2003f0c64dcc099635cdf2d1113bbae99c1
View on Chainz β†—

Height

#87,118

Difficulty

9.280874

Transactions

1

Size

204 B

Version

2

Bits

0947e756

Nonce

7,820

Timestamp

7/28/2013, 3:44:36 PM

Confirmations

6,713,149

Merkle Root

6239c7ba267444e88cf3042dd8bfb616f063b0ed108db508a0a7a1f63de04e2c
Transactions (1)
Coinbase6239c7ba267444…a7a1f63de04e2c
1 in β†’ 1 out11.5900 XPM109 B
AWJdVGNZ…EKN6upBd
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.

4.640 Γ— 10¹⁰⁡(106-digit number)
46400786788873109914…80877651395756016090
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
4.640 Γ— 10¹⁰⁡(106-digit number)
46400786788873109914…80877651395756016089
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.280 Γ— 10¹⁰⁡(106-digit number)
92801573577746219828…61755302791512032179
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.856 Γ— 10¹⁰⁢(107-digit number)
18560314715549243965…23510605583024064359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.712 Γ— 10¹⁰⁢(107-digit number)
37120629431098487931…47021211166048128719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.424 Γ— 10¹⁰⁢(107-digit number)
74241258862196975862…94042422332096257439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.484 Γ— 10¹⁰⁷(108-digit number)
14848251772439395172…88084844664192514879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.969 Γ— 10¹⁰⁷(108-digit number)
29696503544878790345…76169689328385029759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.939 Γ— 10¹⁰⁷(108-digit number)
59393007089757580690…52339378656770059519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.187 Γ— 10¹⁰⁸(109-digit number)
11878601417951516138…04678757313540119039
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 87118

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 7b1e30486b10855922e26dde510db2003f0c64dcc099635cdf2d1113bbae99c1

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 #87,118 on Chainz β†—
Circulating Supply:57,646,193 XPMΒ·at block #6,800,266 Β· updates every 60s
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