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Block #2,634,077

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 6:15:09 PM Β· Difficulty 11.2214 Β· 4,208,113 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0472748837491a755edcd9be31236e1c49da8e9dd60bdae30e377299aa17b133
View on Chainz β†—

Difficulty

11.221435

Transactions

1

Size

201 B

Version

2

Bits

0b38aff4

Nonce

85,949,287

Timestamp

4/28/2018, 6:15:09 PM

Confirmations

4,208,113

Merkle Root

60ce53533e1b3a8eb22e7e27939147ab5c99ef3991bc24a936e41efabc07ba7c
Transactions (1)
Coinbase60ce53533e1b3a…e41efabc07ba7c
1 in β†’ 1 out7.9300 XPM110 B
AWU9QT1M…TXfGqJcJ
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.

4.244 Γ— 10⁹⁢(97-digit number)
42445225362739853623…55491802156488981760
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
4.244 Γ— 10⁹⁢(97-digit number)
42445225362739853623…55491802156488981761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.489 Γ— 10⁹⁢(97-digit number)
84890450725479707247…10983604312977963521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.697 Γ— 10⁹⁷(98-digit number)
16978090145095941449…21967208625955927041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.395 Γ— 10⁹⁷(98-digit number)
33956180290191882899…43934417251911854081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.791 Γ— 10⁹⁷(98-digit number)
67912360580383765798…87868834503823708161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.358 Γ— 10⁹⁸(99-digit number)
13582472116076753159…75737669007647416321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.716 Γ— 10⁹⁸(99-digit number)
27164944232153506319…51475338015294832641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.432 Γ— 10⁹⁸(99-digit number)
54329888464307012638…02950676030589665281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.086 Γ— 10⁹⁹(100-digit number)
10865977692861402527…05901352061179330561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.173 Γ— 10⁹⁹(100-digit number)
21731955385722805055…11802704122358661121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.346 Γ— 10⁹⁹(100-digit number)
43463910771445610110…23605408244717322241
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 2634077

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 0472748837491a755edcd9be31236e1c49da8e9dd60bdae30e377299aa17b133

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 #2,634,077 on Chainz β†—
Circulating Supply:57,981,913 XPMΒ·at block #6,842,189 Β· updates every 60s
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