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Home/Chain Registry/Block #2,732,002

Block #2,732,002

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/3/2018, 4:24:22 AM Β· Difficulty 11.6311 Β· 4,111,039 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
78152f025b832faf7b7a2da0a0ada740e330acddeff4f0730fb5f2f80521fd99
View on Chainz β†—

Difficulty

11.631148

Transactions

1

Size

200 B

Version

2

Bits

0ba192e9

Nonce

394,894,564

Timestamp

7/3/2018, 4:24:22 AM

Confirmations

4,111,039

Merkle Root

23a14ffa659014bbaa1aab3068f42a45a11237b003c30976ee19902cd35d948a
Transactions (1)
Coinbase23a14ffa659014…19902cd35d948a
1 in β†’ 1 out7.3800 XPM110 B
AZtxQr2F…7grUWrUz
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.

2.363 Γ— 10⁹⁡(96-digit number)
23632330069282779736…15480709870246132480
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
2.363 Γ— 10⁹⁡(96-digit number)
23632330069282779736…15480709870246132481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.726 Γ— 10⁹⁡(96-digit number)
47264660138565559472…30961419740492264961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.452 Γ— 10⁹⁡(96-digit number)
94529320277131118945…61922839480984529921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.890 Γ— 10⁹⁢(97-digit number)
18905864055426223789…23845678961969059841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.781 Γ— 10⁹⁢(97-digit number)
37811728110852447578…47691357923938119681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.562 Γ— 10⁹⁢(97-digit number)
75623456221704895156…95382715847876239361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.512 Γ— 10⁹⁷(98-digit number)
15124691244340979031…90765431695752478721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.024 Γ— 10⁹⁷(98-digit number)
30249382488681958062…81530863391504957441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.049 Γ— 10⁹⁷(98-digit number)
60498764977363916125…63061726783009914881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.209 Γ— 10⁹⁸(99-digit number)
12099752995472783225…26123453566019829761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.419 Γ— 10⁹⁸(99-digit number)
24199505990945566450…52246907132039659521
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 2732002

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 78152f025b832faf7b7a2da0a0ada740e330acddeff4f0730fb5f2f80521fd99

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 #2,732,002 on Chainz β†—
Circulating Supply:57,988,685 XPMΒ·at block #6,843,040 Β· updates every 60s
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