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Block #3,153,611

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/24/2019, 4:21:04 PM Β· Difficulty 11.3177 Β· 3,685,581 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d7bcbdd7eddd16152ba1f6830e913b1f1515c99f49c07947bb32d751dd6be5a1
View on Chainz β†—

Difficulty

11.317706

Transactions

1

Size

202 B

Version

2

Bits

0b51552b

Nonce

947,848,225

Timestamp

4/24/2019, 4:21:04 PM

Confirmations

3,685,581

Merkle Root

91da3ac592b8966bb501a57b7860531d996b5275d9d9149309651422f8999fe8
Transactions (1)
Coinbase91da3ac592b896…651422f8999fe8
1 in β†’ 1 out7.7900 XPM110 B
AbXwmGxD…4XXYP765
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.

5.532 Γ— 10⁹⁸(99-digit number)
55324416591918030415…07626437265904947200
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
5.532 Γ— 10⁹⁸(99-digit number)
55324416591918030415…07626437265904947201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.106 Γ— 10⁹⁹(100-digit number)
11064883318383606083…15252874531809894401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.212 Γ— 10⁹⁹(100-digit number)
22129766636767212166…30505749063619788801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.425 Γ— 10⁹⁹(100-digit number)
44259533273534424332…61011498127239577601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.851 Γ— 10⁹⁹(100-digit number)
88519066547068848665…22022996254479155201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.770 Γ— 10¹⁰⁰(101-digit number)
17703813309413769733…44045992508958310401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.540 Γ— 10¹⁰⁰(101-digit number)
35407626618827539466…88091985017916620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.081 Γ— 10¹⁰⁰(101-digit number)
70815253237655078932…76183970035833241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.416 Γ— 10¹⁰¹(102-digit number)
14163050647531015786…52367940071666483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.832 Γ— 10¹⁰¹(102-digit number)
28326101295062031572…04735880143332966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.665 Γ— 10¹⁰¹(102-digit number)
56652202590124063145…09471760286665932801
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 3153611

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 d7bcbdd7eddd16152ba1f6830e913b1f1515c99f49c07947bb32d751dd6be5a1

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 #3,153,611 on Chainz β†—
Circulating Supply:57,957,814 XPMΒ·at block #6,839,191 Β· updates every 60s
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