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Home/Chain Registry/Block #2,656,378

Block #2,656,378

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 5/11/2018, 1:00:26 AM Β· Difficulty 11.6891 Β· 4,177,236 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3c1ec88b541fc1dd548ca6cbe0ff639862f27d5e03ab4d36740601880ae5b3b7
View on Chainz β†—

Difficulty

11.689142

Transactions

1

Size

199 B

Version

2

Bits

0bb06ba2

Nonce

2,055,877,518

Timestamp

5/11/2018, 1:00:26 AM

Confirmations

4,177,236

Merkle Root

ab75b7b9653a6e955cc2cbb033269cb7a7d2a92b60c7360f36142ae4b6f6244a
Transactions (1)
Coinbaseab75b7b9653a6e…142ae4b6f6244a
1 in β†’ 1 out7.3100 XPM110 B
AetHcgV3…WYMxnwfg
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.

1.038 Γ— 10⁹³(94-digit number)
10387966149845294666…35437842019859960000
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
1.038 Γ— 10⁹³(94-digit number)
10387966149845294666…35437842019859959999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.077 Γ— 10⁹³(94-digit number)
20775932299690589332…70875684039719919999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.155 Γ— 10⁹³(94-digit number)
41551864599381178664…41751368079439839999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.310 Γ— 10⁹³(94-digit number)
83103729198762357329…83502736158879679999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.662 Γ— 10⁹⁴(95-digit number)
16620745839752471465…67005472317759359999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.324 Γ— 10⁹⁴(95-digit number)
33241491679504942931…34010944635518719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.648 Γ— 10⁹⁴(95-digit number)
66482983359009885863…68021889271037439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.329 Γ— 10⁹⁡(96-digit number)
13296596671801977172…36043778542074879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.659 Γ— 10⁹⁡(96-digit number)
26593193343603954345…72087557084149759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.318 Γ— 10⁹⁡(96-digit number)
53186386687207908690…44175114168299519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.063 Γ— 10⁹⁢(97-digit number)
10637277337441581738…88350228336599039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
2.127 Γ— 10⁹⁢(97-digit number)
21274554674883163476…76700456673198079999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2656378

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 3c1ec88b541fc1dd548ca6cbe0ff639862f27d5e03ab4d36740601880ae5b3b7

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 #2,656,378 on Chainz β†—
Circulating Supply:57,913,122 XPMΒ·at block #6,833,613 Β· updates every 60s
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