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Home/Chain Registry/Block #2,634,238

Block #2,634,238

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/28/2018, 7:47:06 PM Β· Difficulty 11.2320 Β· 4,207,756 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
df0788835a3ba6bbb03d5dfbcbb254b85b2a80e5a40f355ec0fa475dfcdcf3f8
View on Chainz β†—

Difficulty

11.231983

Transactions

2

Size

1.17 KB

Version

2

Bits

0b3b6335

Nonce

703,829,951

Timestamp

4/28/2018, 7:47:06 PM

Confirmations

4,207,756

Merkle Root

4f2203a155e537e553184037bfed1f3dc575e9439410940ca1b5328dec830120
Transactions (2)
Coinbase33a48d25c1b6be…e2765489d08549
1 in β†’ 1 out7.9400 XPM110 B
Adqah8zh…1WwoHJ9t
b1afe71f885abf…3658ae9c3b355a
6 in β†’ 3 out748.6181 XPM998 B
AMJxCxXM…qw6ErgS2AcU8qK15…8VeYUcQ5AJHHtshE…jc4mKjCY
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.

6.659 Γ— 10⁹⁡(96-digit number)
66592549291031114766…75076492292690344960
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
6.659 Γ— 10⁹⁡(96-digit number)
66592549291031114766…75076492292690344959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.331 Γ— 10⁹⁢(97-digit number)
13318509858206222953…50152984585380689919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.663 Γ— 10⁹⁢(97-digit number)
26637019716412445906…00305969170761379839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.327 Γ— 10⁹⁢(97-digit number)
53274039432824891813…00611938341522759679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.065 Γ— 10⁹⁷(98-digit number)
10654807886564978362…01223876683045519359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.130 Γ— 10⁹⁷(98-digit number)
21309615773129956725…02447753366091038719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.261 Γ— 10⁹⁷(98-digit number)
42619231546259913450…04895506732182077439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.523 Γ— 10⁹⁷(98-digit number)
85238463092519826901…09791013464364154879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.704 Γ— 10⁹⁸(99-digit number)
17047692618503965380…19582026928728309759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.409 Γ— 10⁹⁸(99-digit number)
34095385237007930760…39164053857456619519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.819 Γ— 10⁹⁸(99-digit number)
68190770474015861520…78328107714913239039
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2634238

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 df0788835a3ba6bbb03d5dfbcbb254b85b2a80e5a40f355ec0fa475dfcdcf3f8

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 #2,634,238 on Chainz β†—
Circulating Supply:57,980,340 XPMΒ·at block #6,841,993 Β· updates every 60s
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