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Home/Chain Registry/Block #2,652,010

Block #2,652,010

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/7/2018, 6:43:32 AM Β· Difficulty 11.7475 Β· 4,189,957 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7b2222a8621bae365e4ca5a28d41a0d29aba1ea5ec8822c3f7c4e5fa0df94911
View on Chainz β†—

Difficulty

11.747482

Transactions

3

Size

1.36 KB

Version

2

Bits

0bbf5afe

Nonce

438,950,249

Timestamp

5/7/2018, 6:43:32 AM

Confirmations

4,189,957

Merkle Root

df23b770d04123111f803e7cdfda8ff0cadc069357b3244b3bf9968ff0fc92b1
Transactions (3)
Coinbase4d09b50caaa90f…93c49c8c1007d4
1 in β†’ 1 out7.2500 XPM110 B
AHdhLm5T…P7t87tE7
9fd29977fb3ae3…d5e018baa11ba1
4 in β†’ 2 out8002.8300 XPM671 B
ATZGf5d1…HFFdjUiUALssV9Qd…PvJB43wd
718a296653adb4…b0a2a7cf73eb00
3 in β†’ 2 out1061.4713 XPM522 B
AZDJsni3…piX2JzTTAHNxzG92…HNH3tj8p
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.

3.842 Γ— 10⁹⁡(96-digit number)
38429909845828991895…32289585054342085120
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
3.842 Γ— 10⁹⁡(96-digit number)
38429909845828991895…32289585054342085119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.685 Γ— 10⁹⁡(96-digit number)
76859819691657983790…64579170108684170239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.537 Γ— 10⁹⁢(97-digit number)
15371963938331596758…29158340217368340479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.074 Γ— 10⁹⁢(97-digit number)
30743927876663193516…58316680434736680959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.148 Γ— 10⁹⁢(97-digit number)
61487855753326387032…16633360869473361919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.229 Γ— 10⁹⁷(98-digit number)
12297571150665277406…33266721738946723839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.459 Γ— 10⁹⁷(98-digit number)
24595142301330554812…66533443477893447679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.919 Γ— 10⁹⁷(98-digit number)
49190284602661109625…33066886955786895359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.838 Γ— 10⁹⁷(98-digit number)
98380569205322219251…66133773911573790719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.967 Γ— 10⁹⁸(99-digit number)
19676113841064443850…32267547823147581439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.935 Γ— 10⁹⁸(99-digit number)
39352227682128887700…64535095646295162879
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 2652010

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 7b2222a8621bae365e4ca5a28d41a0d29aba1ea5ec8822c3f7c4e5fa0df94911

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 #2,652,010 on Chainz β†—
Circulating Supply:57,980,119 XPMΒ·at block #6,841,966 Β· updates every 60s
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