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Home/Chain Registry/Block #55,724

Block #55,724

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2013, 3:28:25 AM Β· Difficulty 8.9439 Β· 6,758,124 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
24c4d3ab4b8ff18e25b3d236e55bf3edd43079de1698a754bdfaa1c274ba7a04
View on Chainz β†—

Height

#55,724

Difficulty

8.943924

Transactions

1

Size

200 B

Version

2

Bits

08f1a502

Nonce

652

Timestamp

7/17/2013, 3:28:25 AM

Confirmations

6,758,124

Merkle Root

d2085f34309003f164da33825e877be17f70d753d1051a41d31fb3b4a1638057
Transactions (1)
Coinbased2085f34309003…1fb3b4a1638057
1 in β†’ 1 out12.4800 XPM109 B
AJbz55M2…moHxsz79
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.

2.349 Γ— 10⁹⁢(97-digit number)
23494615527715014313…11168775518628510070
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
2.349 Γ— 10⁹⁢(97-digit number)
23494615527715014313…11168775518628510071
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.698 Γ— 10⁹⁢(97-digit number)
46989231055430028626…22337551037257020141
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.397 Γ— 10⁹⁢(97-digit number)
93978462110860057252…44675102074514040281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.879 Γ— 10⁹⁷(98-digit number)
18795692422172011450…89350204149028080561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.759 Γ— 10⁹⁷(98-digit number)
37591384844344022901…78700408298056161121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.518 Γ— 10⁹⁷(98-digit number)
75182769688688045802…57400816596112322241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.503 Γ— 10⁹⁸(99-digit number)
15036553937737609160…14801633192224644481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.007 Γ— 10⁹⁸(99-digit number)
30073107875475218320…29603266384449288961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 55724

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 24c4d3ab4b8ff18e25b3d236e55bf3edd43079de1698a754bdfaa1c274ba7a04

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 #55,724 on Chainz β†—
Circulating Supply:57,754,854 XPMΒ·at block #6,813,847 Β· updates every 60s
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