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Home/Chain Registry/Block #2,860,368

Block #2,860,368

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/29/2018, 10:23:51 PM Β· Difficulty 11.6750 Β· 3,982,626 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3e5603091193176cd169cb99a71f7460457e2b853aa71b80f337841d3020d844
View on Chainz β†—

Difficulty

11.674967

Transactions

1

Size

201 B

Version

2

Bits

0baccaa4

Nonce

1,974,282,701

Timestamp

9/29/2018, 10:23:51 PM

Confirmations

3,982,626

Merkle Root

8c75e262a4110b26098af70d8f39fb61470ccb8da6dc512b6a6a1b4c7bb80923
Transactions (1)
Coinbase8c75e262a4110b…6a1b4c7bb80923
1 in β†’ 1 out7.3200 XPM110 B
AX1cg7uZ…8pr3CfKP
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.

7.504 Γ— 10⁹⁢(97-digit number)
75042820809560613433…45409949304659251200
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
7.504 Γ— 10⁹⁢(97-digit number)
75042820809560613433…45409949304659251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.500 Γ— 10⁹⁷(98-digit number)
15008564161912122686…90819898609318502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.001 Γ— 10⁹⁷(98-digit number)
30017128323824245373…81639797218637004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.003 Γ— 10⁹⁷(98-digit number)
60034256647648490747…63279594437274009601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.200 Γ— 10⁹⁸(99-digit number)
12006851329529698149…26559188874548019201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.401 Γ— 10⁹⁸(99-digit number)
24013702659059396298…53118377749096038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.802 Γ— 10⁹⁸(99-digit number)
48027405318118792597…06236755498192076801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.605 Γ— 10⁹⁸(99-digit number)
96054810636237585195…12473510996384153601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.921 Γ— 10⁹⁹(100-digit number)
19210962127247517039…24947021992768307201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.842 Γ— 10⁹⁹(100-digit number)
38421924254495034078…49894043985536614401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.684 Γ— 10⁹⁹(100-digit number)
76843848508990068156…99788087971073228801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.536 Γ— 10¹⁰⁰(101-digit number)
15368769701798013631…99576175942146457601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2860368

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 3e5603091193176cd169cb99a71f7460457e2b853aa71b80f337841d3020d844

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 #2,860,368 on Chainz β†—
Circulating Supply:57,988,309 XPMΒ·at block #6,842,993 Β· updates every 60s
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