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Home/Chain Registry/Block #2,702,964

Block #2,702,964

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/13/2018, 12:13:09 AM Β· Difficulty 11.6311 Β· 4,138,029 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
995e7b762725e82aeda73ee49cdb3d992653500d13a0893566647b880b935796
View on Chainz β†—

Difficulty

11.631133

Transactions

1

Size

199 B

Version

2

Bits

0ba191ef

Nonce

1,233,828,762

Timestamp

6/13/2018, 12:13:09 AM

Confirmations

4,138,029

Merkle Root

c2b6c1123727c22ee132766656799f4d33dd1b02031a16210bfb215ed07fe989
Transactions (1)
Coinbasec2b6c1123727c2…fb215ed07fe989
1 in β†’ 1 out7.3800 XPM110 B
AczyRQNi…FFB1GnAH
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.

4.403 Γ— 10⁹²(93-digit number)
44038842117525750320…04107434278606964780
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
4.403 Γ— 10⁹²(93-digit number)
44038842117525750320…04107434278606964779
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.807 Γ— 10⁹²(93-digit number)
88077684235051500640…08214868557213929559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.761 Γ— 10⁹³(94-digit number)
17615536847010300128…16429737114427859119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.523 Γ— 10⁹³(94-digit number)
35231073694020600256…32859474228855718239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.046 Γ— 10⁹³(94-digit number)
70462147388041200512…65718948457711436479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.409 Γ— 10⁹⁴(95-digit number)
14092429477608240102…31437896915422872959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.818 Γ— 10⁹⁴(95-digit number)
28184858955216480204…62875793830845745919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.636 Γ— 10⁹⁴(95-digit number)
56369717910432960409…25751587661691491839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.127 Γ— 10⁹⁡(96-digit number)
11273943582086592081…51503175323382983679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.254 Γ— 10⁹⁡(96-digit number)
22547887164173184163…03006350646765967359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.509 Γ— 10⁹⁡(96-digit number)
45095774328346368327…06012701293531934719
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 2702964

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 995e7b762725e82aeda73ee49cdb3d992653500d13a0893566647b880b935796

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 #2,702,964 on Chainz β†—
Circulating Supply:57,972,299 XPMΒ·at block #6,840,992 Β· updates every 60s
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