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Home/Chain Registry/Block #2,783,346

Block #2,783,346

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2018, 12:56:08 PM Β· Difficulty 11.6632 Β· 4,061,245 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
48a51b498518dfc83f8f2f02775a1378b1fadeaa87b1428779137d01c8ec72d9
View on Chainz β†—

Difficulty

11.663212

Transactions

1

Size

200 B

Version

2

Bits

0ba9c83d

Nonce

250,286,798

Timestamp

8/7/2018, 12:56:08 PM

Confirmations

4,061,245

Merkle Root

09841ffcbc177132df9a3b54adf5a38f58a1c657d218fda068ead04699b324df
Transactions (1)
Coinbase09841ffcbc1771…ead04699b324df
1 in β†’ 1 out7.3400 XPM110 B
AbDPfySz…CQVAsgih
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.

8.361 Γ— 10⁹⁴(95-digit number)
83610234527944952832…95669560628167004160
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
8.361 Γ— 10⁹⁴(95-digit number)
83610234527944952832…95669560628167004159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.672 Γ— 10⁹⁡(96-digit number)
16722046905588990566…91339121256334008319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.344 Γ— 10⁹⁡(96-digit number)
33444093811177981133…82678242512668016639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.688 Γ— 10⁹⁡(96-digit number)
66888187622355962266…65356485025336033279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.337 Γ— 10⁹⁢(97-digit number)
13377637524471192453…30712970050672066559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.675 Γ— 10⁹⁢(97-digit number)
26755275048942384906…61425940101344133119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.351 Γ— 10⁹⁢(97-digit number)
53510550097884769812…22851880202688266239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.070 Γ— 10⁹⁷(98-digit number)
10702110019576953962…45703760405376532479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.140 Γ— 10⁹⁷(98-digit number)
21404220039153907925…91407520810753064959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.280 Γ— 10⁹⁷(98-digit number)
42808440078307815850…82815041621506129919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.561 Γ— 10⁹⁷(98-digit number)
85616880156615631700…65630083243012259839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.712 Γ— 10⁹⁸(99-digit number)
17123376031323126340…31260166486024519679
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 2783346

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 48a51b498518dfc83f8f2f02775a1378b1fadeaa87b1428779137d01c8ec72d9

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 #2,783,346 on Chainz β†—
Circulating Supply:58,001,137 XPMΒ·at block #6,844,590 Β· updates every 60s
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