XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #53,761

Block #53,761

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 4:53:41 PM Β· Difficulty 8.9269 Β· 6,751,324 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
64f9761dd397beb5f9aee2b875c467fc5a0cb975619bff62dce7ffa5eb9415c6
View on Chainz β†—

Height

#53,761

Difficulty

8.926945

Transactions

1

Size

198 B

Version

2

Bits

08ed4c49

Nonce

416

Timestamp

7/16/2013, 4:53:41 PM

Confirmations

6,751,324

Merkle Root

05bdac6679285426370e4b99ff8b9d1f197e9423a5db180952184247dc6221cc
Transactions (1)
Coinbase05bdac66792854…184247dc6221cc
1 in β†’ 1 out12.5300 XPM110 B
AX85bWR1…X2GwLbPj
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.

5.051 Γ— 10⁹⁰(91-digit number)
50514921321429383647…07010349212616224420
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
5.051 Γ— 10⁹⁰(91-digit number)
50514921321429383647…07010349212616224421
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.010 Γ— 10⁹¹(92-digit number)
10102984264285876729…14020698425232448841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.020 Γ— 10⁹¹(92-digit number)
20205968528571753459…28041396850464897681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.041 Γ— 10⁹¹(92-digit number)
40411937057143506918…56082793700929795361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.082 Γ— 10⁹¹(92-digit number)
80823874114287013836…12165587401859590721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.616 Γ— 10⁹²(93-digit number)
16164774822857402767…24331174803719181441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.232 Γ— 10⁹²(93-digit number)
32329549645714805534…48662349607438362881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.465 Γ— 10⁹²(93-digit number)
64659099291429611069…97324699214876725761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.293 Γ— 10⁹³(94-digit number)
12931819858285922213…94649398429753451521
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 53761

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 64f9761dd397beb5f9aee2b875c467fc5a0cb975619bff62dce7ffa5eb9415c6

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 #53,761 on Chainz β†—
Circulating Supply:57,684,745 XPMΒ·at block #6,805,084 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