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Home/Chain Registry/Block #2,639,797

Block #2,639,797

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 6:56:53 PM Β· Difficulty 11.5532 Β· 4,193,083 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
70d1512e3948f058841bc4d0720a62acd4d8ebf8ab30b74ec8d7aaf4eb5d54f3
View on Chainz β†—

Difficulty

11.553248

Transactions

1

Size

201 B

Version

2

Bits

0b8da1ae

Nonce

1,250,837,692

Timestamp

4/30/2018, 6:56:53 PM

Confirmations

4,193,083

Merkle Root

ead38756738b8c17527fb55092ac8edadac25e51fe1ef21a00db016bb219c816
Transactions (1)
Coinbaseead38756738b8c…db016bb219c816
1 in β†’ 1 out7.4800 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.

2.419 Γ— 10⁹⁢(97-digit number)
24190489430836012863…06839984392427704320
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
2.419 Γ— 10⁹⁢(97-digit number)
24190489430836012863…06839984392427704319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.838 Γ— 10⁹⁢(97-digit number)
48380978861672025727…13679968784855408639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.676 Γ— 10⁹⁢(97-digit number)
96761957723344051454…27359937569710817279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.935 Γ— 10⁹⁷(98-digit number)
19352391544668810290…54719875139421634559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.870 Γ— 10⁹⁷(98-digit number)
38704783089337620581…09439750278843269119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.740 Γ— 10⁹⁷(98-digit number)
77409566178675241163…18879500557686538239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.548 Γ— 10⁹⁸(99-digit number)
15481913235735048232…37759001115373076479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.096 Γ— 10⁹⁸(99-digit number)
30963826471470096465…75518002230746152959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.192 Γ— 10⁹⁸(99-digit number)
61927652942940192930…51036004461492305919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.238 Γ— 10⁹⁹(100-digit number)
12385530588588038586…02072008922984611839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.477 Γ— 10⁹⁹(100-digit number)
24771061177176077172…04144017845969223679
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 2639797

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 70d1512e3948f058841bc4d0720a62acd4d8ebf8ab30b74ec8d7aaf4eb5d54f3

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 #2,639,797 on Chainz β†—
Circulating Supply:57,907,210 XPMΒ·at block #6,832,879 Β· updates every 60s
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