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Home/Chain Registry/Block #2,752,344

Block #2,752,344

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2018, 3:24:37 AM Β· Difficulty 11.6492 Β· 4,085,898 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d64bbad182fba153fb54618faf735be3044a3508b7389c378f7dbbb00cd1f68f
View on Chainz β†—

Difficulty

11.649182

Transactions

1

Size

201 B

Version

2

Bits

0ba630d1

Nonce

561,478,847

Timestamp

7/17/2018, 3:24:37 AM

Confirmations

4,085,898

Merkle Root

71e111daaf3bb9b5a50aca67ee12db5fd5d92b999151e420653af1a77e260db0
Transactions (1)
Coinbase71e111daaf3bb9…3af1a77e260db0
1 in β†’ 1 out7.3600 XPM110 B
AVCWoJgq…SzgYNLKv
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.

2.626 Γ— 10⁹⁢(97-digit number)
26267959669163391543…61007756384211165440
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
2.626 Γ— 10⁹⁢(97-digit number)
26267959669163391543…61007756384211165441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.253 Γ— 10⁹⁢(97-digit number)
52535919338326783086…22015512768422330881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.050 Γ— 10⁹⁷(98-digit number)
10507183867665356617…44031025536844661761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.101 Γ— 10⁹⁷(98-digit number)
21014367735330713234…88062051073689323521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.202 Γ— 10⁹⁷(98-digit number)
42028735470661426469…76124102147378647041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.405 Γ— 10⁹⁷(98-digit number)
84057470941322852938…52248204294757294081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.681 Γ— 10⁹⁸(99-digit number)
16811494188264570587…04496408589514588161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.362 Γ— 10⁹⁸(99-digit number)
33622988376529141175…08992817179029176321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.724 Γ— 10⁹⁸(99-digit number)
67245976753058282351…17985634358058352641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.344 Γ— 10⁹⁹(100-digit number)
13449195350611656470…35971268716116705281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.689 Γ— 10⁹⁹(100-digit number)
26898390701223312940…71942537432233410561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2752344

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 d64bbad182fba153fb54618faf735be3044a3508b7389c378f7dbbb00cd1f68f

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 #2,752,344 on Chainz β†—
Circulating Supply:57,950,212 XPMΒ·at block #6,838,241 Β· updates every 60s
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