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Home/Chain Registry/Block #3,154,318

Block #3,154,318

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/25/2019, 4:04:17 AM Β· Difficulty 11.3184 Β· 3,689,380 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9505e55c079d9be477f919f07ff7c8522bcc43d0595ee24609b0610acbc2d938
View on Chainz β†—

Difficulty

11.318383

Transactions

1

Size

200 B

Version

2

Bits

0b518185

Nonce

1,488,591,044

Timestamp

4/25/2019, 4:04:17 AM

Confirmations

3,689,380

Merkle Root

8ca2689cc75a43bf8f8693ea2bb6a0ac9cc109c928c89254a1b7bbd580e9ff62
Transactions (1)
Coinbase8ca2689cc75a43…b7bbd580e9ff62
1 in β†’ 1 out7.7900 XPM110 B
AUMQRepm…tAfKmdW1
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.

5.636 Γ— 10⁹³(94-digit number)
56368436953228484107…36505651435537766400
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
5.636 Γ— 10⁹³(94-digit number)
56368436953228484107…36505651435537766401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.127 Γ— 10⁹⁴(95-digit number)
11273687390645696821…73011302871075532801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.254 Γ— 10⁹⁴(95-digit number)
22547374781291393642…46022605742151065601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.509 Γ— 10⁹⁴(95-digit number)
45094749562582787285…92045211484302131201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.018 Γ— 10⁹⁴(95-digit number)
90189499125165574571…84090422968604262401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.803 Γ— 10⁹⁡(96-digit number)
18037899825033114914…68180845937208524801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.607 Γ— 10⁹⁡(96-digit number)
36075799650066229828…36361691874417049601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.215 Γ— 10⁹⁡(96-digit number)
72151599300132459657…72723383748834099201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.443 Γ— 10⁹⁢(97-digit number)
14430319860026491931…45446767497668198401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.886 Γ— 10⁹⁢(97-digit number)
28860639720052983862…90893534995336396801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.772 Γ— 10⁹⁢(97-digit number)
57721279440105967725…81787069990672793601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.154 Γ— 10⁹⁷(98-digit number)
11544255888021193545…63574139981345587201
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 3154318

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 9505e55c079d9be477f919f07ff7c8522bcc43d0595ee24609b0610acbc2d938

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 #3,154,318 on Chainz β†—
Circulating Supply:57,993,952 XPMΒ·at block #6,843,697 Β· updates every 60s
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