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Home/Chain Registry/Block #3,505,247

Block #3,505,247

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/8/2020, 11:51:38 AM Β· Difficulty 10.9306 Β· 3,339,642 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e034d2df8d48246bc8213208a247fcfb2f463cb0e22fe5f3d4dab3e17fd23a62
View on Chainz β†—

Difficulty

10.930593

Transactions

1

Size

199 B

Version

2

Bits

0aee3b5f

Nonce

1,341,071,929

Timestamp

1/8/2020, 11:51:38 AM

Confirmations

3,339,642

Merkle Root

a8d061b457ee9b2473f3865f08244ce17559e740302354dd874b1a96af5b12f8
Transactions (1)
Coinbasea8d061b457ee9b…4b1a96af5b12f8
1 in β†’ 1 out8.3600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

1.031 Γ— 10⁹³(94-digit number)
10316074729127844891…91054293953685455360
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
1.031 Γ— 10⁹³(94-digit number)
10316074729127844891…91054293953685455361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.063 Γ— 10⁹³(94-digit number)
20632149458255689783…82108587907370910721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.126 Γ— 10⁹³(94-digit number)
41264298916511379567…64217175814741821441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.252 Γ— 10⁹³(94-digit number)
82528597833022759135…28434351629483642881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.650 Γ— 10⁹⁴(95-digit number)
16505719566604551827…56868703258967285761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.301 Γ— 10⁹⁴(95-digit number)
33011439133209103654…13737406517934571521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.602 Γ— 10⁹⁴(95-digit number)
66022878266418207308…27474813035869143041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.320 Γ— 10⁹⁡(96-digit number)
13204575653283641461…54949626071738286081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.640 Γ— 10⁹⁡(96-digit number)
26409151306567282923…09899252143476572161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.281 Γ— 10⁹⁡(96-digit number)
52818302613134565846…19798504286953144321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.056 Γ— 10⁹⁢(97-digit number)
10563660522626913169…39597008573906288641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
2.112 Γ— 10⁹⁢(97-digit number)
21127321045253826338…79194017147812577281
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 3505247

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 e034d2df8d48246bc8213208a247fcfb2f463cb0e22fe5f3d4dab3e17fd23a62

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 #3,505,247 on Chainz β†—
Circulating Supply:58,003,527 XPMΒ·at block #6,844,888 Β· updates every 60s
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