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Home/Chain Registry/Block #2,771,816

Block #2,771,816

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/30/2018, 1:12:39 PM Β· Difficulty 11.6614 Β· 4,068,169 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d98724cd6aab0a2f497907c3c081b1be900cf40aa875c68fb96a92272a39f8d8
View on Chainz β†—

Difficulty

11.661383

Transactions

1

Size

201 B

Version

2

Bits

0ba95064

Nonce

1,308,325,513

Timestamp

7/30/2018, 1:12:39 PM

Confirmations

4,068,169

Merkle Root

ef07ac7f7c6e353ccb84fedc64d748c72bfa75db9f5150f00cb6d0192ccb2d27
Transactions (1)
Coinbaseef07ac7f7c6e35…b6d0192ccb2d27
1 in β†’ 1 out7.3400 XPM110 B
APGz7NHf…Q6zzfKio
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.

5.784 Γ— 10⁹⁢(97-digit number)
57840197707317305708…64631543509242337280
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
5.784 Γ— 10⁹⁢(97-digit number)
57840197707317305708…64631543509242337279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.156 Γ— 10⁹⁷(98-digit number)
11568039541463461141…29263087018484674559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.313 Γ— 10⁹⁷(98-digit number)
23136079082926922283…58526174036969349119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.627 Γ— 10⁹⁷(98-digit number)
46272158165853844567…17052348073938698239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.254 Γ— 10⁹⁷(98-digit number)
92544316331707689134…34104696147877396479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.850 Γ— 10⁹⁸(99-digit number)
18508863266341537826…68209392295754792959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.701 Γ— 10⁹⁸(99-digit number)
37017726532683075653…36418784591509585919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.403 Γ— 10⁹⁸(99-digit number)
74035453065366151307…72837569183019171839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.480 Γ— 10⁹⁹(100-digit number)
14807090613073230261…45675138366038343679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.961 Γ— 10⁹⁹(100-digit number)
29614181226146460522…91350276732076687359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.922 Γ— 10⁹⁹(100-digit number)
59228362452292921045…82700553464153374719
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 2771816

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 d98724cd6aab0a2f497907c3c081b1be900cf40aa875c68fb96a92272a39f8d8

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 #2,771,816 on Chainz β†—
Circulating Supply:57,964,188 XPMΒ·at block #6,839,984 Β· updates every 60s
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