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Home/Chain Registry/Block #3,244,950

Block #3,244,950

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/28/2019, 4:55:27 PM Β· Difficulty 11.0133 Β· 3,556,500 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1213af4c7a64d5040ec00bd698e85cba2c68407e0ded096adbfb89d24a3f57b8
View on Chainz β†—

Difficulty

11.013330

Transactions

1

Size

199 B

Version

2

Bits

0b036997

Nonce

606,566,997

Timestamp

6/28/2019, 4:55:27 PM

Confirmations

3,556,500

Merkle Root

57376edefe2445e7f48e02aacc7d7adbdd79e47a9ad614221ec1f09e7480abdb
Transactions (1)
Coinbase57376edefe2445…c1f09e7480abdb
1 in β†’ 1 out8.2300 XPM109 B
ARbm48qR…9xQc8DBX
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.

3.111 Γ— 10⁹⁡(96-digit number)
31112467013042541624…52438436380218656000
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
3.111 Γ— 10⁹⁡(96-digit number)
31112467013042541624…52438436380218656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.222 Γ— 10⁹⁡(96-digit number)
62224934026085083248…04876872760437312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.244 Γ— 10⁹⁢(97-digit number)
12444986805217016649…09753745520874624001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.488 Γ— 10⁹⁢(97-digit number)
24889973610434033299…19507491041749248001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.977 Γ— 10⁹⁢(97-digit number)
49779947220868066599…39014982083498496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.955 Γ— 10⁹⁢(97-digit number)
99559894441736133198…78029964166996992001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.991 Γ— 10⁹⁷(98-digit number)
19911978888347226639…56059928333993984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.982 Γ— 10⁹⁷(98-digit number)
39823957776694453279…12119856667987968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.964 Γ— 10⁹⁷(98-digit number)
79647915553388906558…24239713335975936001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.592 Γ— 10⁹⁸(99-digit number)
15929583110677781311…48479426671951872001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.185 Γ— 10⁹⁸(99-digit number)
31859166221355562623…96958853343903744001
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 3244950

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 1213af4c7a64d5040ec00bd698e85cba2c68407e0ded096adbfb89d24a3f57b8

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 #3,244,950 on Chainz β†—
Circulating Supply:57,655,673 XPMΒ·at block #6,801,449 Β· updates every 60s
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