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Home/Chain Registry/Block #2,621,177

Block #2,621,177

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/19/2018, 6:02:10 PM Β· Difficulty 11.2320 Β· 4,205,224 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a866c4caabf4a4e4c4c3e946916b18f7d5be6a3cc758511ab7d5c10c4f1db6c1
View on Chainz β†—

Difficulty

11.232025

Transactions

1

Size

201 B

Version

2

Bits

0b3b65f9

Nonce

1,866,339,247

Timestamp

4/19/2018, 6:02:10 PM

Confirmations

4,205,224

Merkle Root

9098d8a7ad9d2c78b8d150bda53f8cb41c34bef3a1d828747351d9fe7f53c527
Transactions (1)
Coinbase9098d8a7ad9d2c…51d9fe7f53c527
1 in β†’ 1 out7.9100 XPM110 B
AbmUcUqM…2NrLzrvU
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.

6.125 Γ— 10⁹⁢(97-digit number)
61250812485074893963…97470576537246012160
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
6.125 Γ— 10⁹⁢(97-digit number)
61250812485074893963…97470576537246012161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.225 Γ— 10⁹⁷(98-digit number)
12250162497014978792…94941153074492024321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.450 Γ— 10⁹⁷(98-digit number)
24500324994029957585…89882306148984048641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.900 Γ— 10⁹⁷(98-digit number)
49000649988059915171…79764612297968097281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.800 Γ— 10⁹⁷(98-digit number)
98001299976119830342…59529224595936194561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.960 Γ— 10⁹⁸(99-digit number)
19600259995223966068…19058449191872389121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.920 Γ— 10⁹⁸(99-digit number)
39200519990447932136…38116898383744778241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.840 Γ— 10⁹⁸(99-digit number)
78401039980895864273…76233796767489556481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.568 Γ— 10⁹⁹(100-digit number)
15680207996179172854…52467593534979112961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.136 Γ— 10⁹⁹(100-digit number)
31360415992358345709…04935187069958225921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.272 Γ— 10⁹⁹(100-digit number)
62720831984716691419…09870374139916451841
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 2621177

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 a866c4caabf4a4e4c4c3e946916b18f7d5be6a3cc758511ab7d5c10c4f1db6c1

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 #2,621,177 on Chainz β†—
Circulating Supply:57,855,339 XPMΒ·at block #6,826,400 Β· updates every 60s
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