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Home/Chain Registry/Block #2,634,620

Block #2,634,620

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 11:22:21 PM Β· Difficulty 11.2569 Β· 4,208,216 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
593f55c8d548784b6e30901b0849659a5aacead106c8c92ba11ac9ed67f7077e
View on Chainz β†—

Difficulty

11.256942

Transactions

1

Size

201 B

Version

2

Bits

0b41c6f4

Nonce

125,637,585

Timestamp

4/28/2018, 11:22:21 PM

Confirmations

4,208,216

Merkle Root

9af652d148d27fcf0a833f9709c6ed56ba136d681910bb2a19787bcad6277893
Transactions (1)
Coinbase9af652d148d27f…787bcad6277893
1 in β†’ 1 out7.8800 XPM110 B
ANJRwJxY…vzLaFE6b
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.

3.190 Γ— 10⁹⁢(97-digit number)
31909219957019204184…22591168681674383360
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
3.190 Γ— 10⁹⁢(97-digit number)
31909219957019204184…22591168681674383361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.381 Γ— 10⁹⁢(97-digit number)
63818439914038408369…45182337363348766721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.276 Γ— 10⁹⁷(98-digit number)
12763687982807681673…90364674726697533441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.552 Γ— 10⁹⁷(98-digit number)
25527375965615363347…80729349453395066881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.105 Γ— 10⁹⁷(98-digit number)
51054751931230726695…61458698906790133761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.021 Γ— 10⁹⁸(99-digit number)
10210950386246145339…22917397813580267521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.042 Γ— 10⁹⁸(99-digit number)
20421900772492290678…45834795627160535041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.084 Γ— 10⁹⁸(99-digit number)
40843801544984581356…91669591254321070081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.168 Γ— 10⁹⁸(99-digit number)
81687603089969162713…83339182508642140161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.633 Γ— 10⁹⁹(100-digit number)
16337520617993832542…66678365017284280321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.267 Γ— 10⁹⁹(100-digit number)
32675041235987665085…33356730034568560641
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 2634620

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 593f55c8d548784b6e30901b0849659a5aacead106c8c92ba11ac9ed67f7077e

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 #2,634,620 on Chainz β†—
Circulating Supply:57,987,032 XPMΒ·at block #6,842,835 Β· updates every 60s
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