XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #59,852

Block #59,852

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2013, 4:41:08 AM Β· Difficulty 8.9667 Β· 6,735,676 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4a6dfea91d55139d4f4bb11c44934304dacdad36e9f7560d49049cc23133b7c5
View on Chainz β†—

Height

#59,852

Difficulty

8.966725

Transactions

1

Size

199 B

Version

2

Bits

08f77b50

Nonce

72

Timestamp

7/18/2013, 4:41:08 AM

Confirmations

6,735,676

Merkle Root

f4799e16c794246d65f280a51424689630720fff18c7c26bf980e4325b3adbb1
Transactions (1)
Coinbasef4799e16c79424…80e4325b3adbb1
1 in β†’ 1 out12.4200 XPM110 B
AGL1rVxw…XHbRJvje
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.

2.699 Γ— 10⁹³(94-digit number)
26992560319278939931…17032361155071241600
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.699 Γ— 10⁹³(94-digit number)
26992560319278939931…17032361155071241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.398 Γ— 10⁹³(94-digit number)
53985120638557879862…34064722310142483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.079 Γ— 10⁹⁴(95-digit number)
10797024127711575972…68129444620284966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.159 Γ— 10⁹⁴(95-digit number)
21594048255423151945…36258889240569932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.318 Γ— 10⁹⁴(95-digit number)
43188096510846303890…72517778481139865601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.637 Γ— 10⁹⁴(95-digit number)
86376193021692607780…45035556962279731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.727 Γ— 10⁹⁡(96-digit number)
17275238604338521556…90071113924559462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.455 Γ— 10⁹⁡(96-digit number)
34550477208677043112…80142227849118924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.910 Γ— 10⁹⁡(96-digit number)
69100954417354086224…60284455698237849601
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 59852

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 4a6dfea91d55139d4f4bb11c44934304dacdad36e9f7560d49049cc23133b7c5

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 #59,852 on Chainz β†—
Circulating Supply:57,608,286 XPMΒ·at block #6,795,527 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