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Home/Chain Registry/Block #2,652,867

Block #2,652,867

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/7/2018, 10:59:55 PM Β· Difficulty 11.7413 Β· 4,185,135 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5d7a5bcf41fb0ab1324a7712fbc8096c6dddf50ca017885bd8f9fadda1ac080e
View on Chainz β†—

Difficulty

11.741338

Transactions

1

Size

200 B

Version

2

Bits

0bbdc857

Nonce

87,811,275

Timestamp

5/7/2018, 10:59:55 PM

Confirmations

4,185,135

Merkle Root

c61b4217a68fd1837a7584eb34ce78d0580f0685a6f8651039fb98296f77ce00
Transactions (1)
Coinbasec61b4217a68fd1…fb98296f77ce00
1 in β†’ 1 out7.2400 XPM110 B
Adqah8zh…1WwoHJ9t
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.

5.020 Γ— 10⁹⁡(96-digit number)
50203425691773077574…07218750208335313920
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
5.020 Γ— 10⁹⁡(96-digit number)
50203425691773077574…07218750208335313919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.004 Γ— 10⁹⁢(97-digit number)
10040685138354615514…14437500416670627839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.008 Γ— 10⁹⁢(97-digit number)
20081370276709231029…28875000833341255679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.016 Γ— 10⁹⁢(97-digit number)
40162740553418462059…57750001666682511359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.032 Γ— 10⁹⁢(97-digit number)
80325481106836924119…15500003333365022719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.606 Γ— 10⁹⁷(98-digit number)
16065096221367384823…31000006666730045439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.213 Γ— 10⁹⁷(98-digit number)
32130192442734769647…62000013333460090879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.426 Γ— 10⁹⁷(98-digit number)
64260384885469539295…24000026666920181759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.285 Γ— 10⁹⁸(99-digit number)
12852076977093907859…48000053333840363519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.570 Γ— 10⁹⁸(99-digit number)
25704153954187815718…96000106667680727039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.140 Γ— 10⁹⁸(99-digit number)
51408307908375631436…92000213335361454079
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 2652867

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 5d7a5bcf41fb0ab1324a7712fbc8096c6dddf50ca017885bd8f9fadda1ac080e

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 #2,652,867 on Chainz β†—
Circulating Supply:57,948,368 XPMΒ·at block #6,838,001 Β· updates every 60s
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