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Home/Chain Registry/Block #2,652,008

Block #2,652,008

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/7/2018, 6:39:47 AM Β· Difficulty 11.7475 Β· 4,191,682 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e7d874aa3ef7a8440ad18e1ec8278823129f4dd6b3431b1c89d8bbeed2f1b2f7
View on Chainz β†—

Difficulty

11.747480

Transactions

1

Size

201 B

Version

2

Bits

0bbf5ad3

Nonce

932,572,496

Timestamp

5/7/2018, 6:39:47 AM

Confirmations

4,191,682

Merkle Root

dce23a9b414040535b6164c90481664d7dfa3f7d8583886d48a8732ed6d78a0c
Transactions (1)
Coinbasedce23a9b414040…a8732ed6d78a0c
1 in β†’ 1 out7.2300 XPM110 B
ALEH19g9…movB2dDa
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.

3.361 Γ— 10⁹⁢(97-digit number)
33618196183259508139…81396584611382922240
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
3.361 Γ— 10⁹⁢(97-digit number)
33618196183259508139…81396584611382922239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.723 Γ— 10⁹⁢(97-digit number)
67236392366519016278…62793169222765844479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.344 Γ— 10⁹⁷(98-digit number)
13447278473303803255…25586338445531688959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.689 Γ— 10⁹⁷(98-digit number)
26894556946607606511…51172676891063377919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.378 Γ— 10⁹⁷(98-digit number)
53789113893215213022…02345353782126755839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.075 Γ— 10⁹⁸(99-digit number)
10757822778643042604…04690707564253511679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.151 Γ— 10⁹⁸(99-digit number)
21515645557286085209…09381415128507023359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.303 Γ— 10⁹⁸(99-digit number)
43031291114572170418…18762830257014046719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.606 Γ— 10⁹⁸(99-digit number)
86062582229144340836…37525660514028093439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.721 Γ— 10⁹⁹(100-digit number)
17212516445828868167…75051321028056186879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.442 Γ— 10⁹⁹(100-digit number)
34425032891657736334…50102642056112373759
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 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
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 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 2652008

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 e7d874aa3ef7a8440ad18e1ec8278823129f4dd6b3431b1c89d8bbeed2f1b2f7

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 #2,652,008 on Chainz β†—
Circulating Supply:57,993,891 XPMΒ·at block #6,843,689 Β· updates every 60s
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