XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #62,939

Block #62,939

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2013, 10:17:32 PM Β· Difficulty 8.9778 Β· 6,731,603 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
65c6738f5dce968f0ba1bc48e6f7e9a935b66c550921aff79e20beaf2a988f90
View on Chainz β†—

Height

#62,939

Difficulty

8.977818

Transactions

1

Size

202 B

Version

2

Bits

08fa5250

Nonce

710

Timestamp

7/18/2013, 10:17:32 PM

Confirmations

6,731,603

Merkle Root

f922fdb0e163f3e84fc93dbd25484393020cf6a09c185968885aee01b8e1c046
Transactions (1)
Coinbasef922fdb0e163f3…5aee01b8e1c046
1 in β†’ 1 out12.3900 XPM110 B
AYGjxbdf…YFHt1cSm
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.

2.523 Γ— 10⁹⁸(99-digit number)
25237162621978371069…61485567362814220000
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
2.523 Γ— 10⁹⁸(99-digit number)
25237162621978371069…61485567362814219999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.047 Γ— 10⁹⁸(99-digit number)
50474325243956742138…22971134725628439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.009 Γ— 10⁹⁹(100-digit number)
10094865048791348427…45942269451256879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.018 Γ— 10⁹⁹(100-digit number)
20189730097582696855…91884538902513759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.037 Γ— 10⁹⁹(100-digit number)
40379460195165393710…83769077805027519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.075 Γ— 10⁹⁹(100-digit number)
80758920390330787421…67538155610055039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.615 Γ— 10¹⁰⁰(101-digit number)
16151784078066157484…35076311220110079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.230 Γ— 10¹⁰⁰(101-digit number)
32303568156132314968…70152622440220159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.460 Γ— 10¹⁰⁰(101-digit number)
64607136312264629937…40305244880440319999
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 62939

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 65c6738f5dce968f0ba1bc48e6f7e9a935b66c550921aff79e20beaf2a988f90

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 #62,939 on Chainz β†—
Circulating Supply:57,600,378 XPMΒ·at block #6,794,541 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK