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Home/Chain Registry/Block #2,761,945

Block #2,761,945

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/23/2018, 6:19:17 PM Β· Difficulty 11.6541 Β· 4,069,931 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ad77706c0e8ab7af4c5dc1ff05a7b30dbc7cef8b433749d16c583d14b8683db8
View on Chainz β†—

Difficulty

11.654133

Transactions

1

Size

200 B

Version

2

Bits

0ba77543

Nonce

875,354,081

Timestamp

7/23/2018, 6:19:17 PM

Confirmations

4,069,931

Merkle Root

7ec073fa3fe1ff3dff6b6cf416495b44815e76f5b4f57ff936c87ae6dcf93446
Transactions (1)
Coinbase7ec073fa3fe1ff…c87ae6dcf93446
1 in β†’ 1 out7.3500 XPM110 B
AehGACai…ZjAAqLAv
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.

7.340 Γ— 10⁹³(94-digit number)
73405692205332003787…97261725081412581120
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
7.340 Γ— 10⁹³(94-digit number)
73405692205332003787…97261725081412581119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.468 Γ— 10⁹⁴(95-digit number)
14681138441066400757…94523450162825162239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.936 Γ— 10⁹⁴(95-digit number)
29362276882132801514…89046900325650324479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.872 Γ— 10⁹⁴(95-digit number)
58724553764265603029…78093800651300648959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.174 Γ— 10⁹⁡(96-digit number)
11744910752853120605…56187601302601297919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.348 Γ— 10⁹⁡(96-digit number)
23489821505706241211…12375202605202595839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.697 Γ— 10⁹⁡(96-digit number)
46979643011412482423…24750405210405191679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.395 Γ— 10⁹⁡(96-digit number)
93959286022824964847…49500810420810383359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.879 Γ— 10⁹⁢(97-digit number)
18791857204564992969…99001620841620766719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.758 Γ— 10⁹⁢(97-digit number)
37583714409129985939…98003241683241533439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.516 Γ— 10⁹⁢(97-digit number)
75167428818259971878…96006483366483066879
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 2761945

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 ad77706c0e8ab7af4c5dc1ff05a7b30dbc7cef8b433749d16c583d14b8683db8

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 #2,761,945 on Chainz β†—
Circulating Supply:57,899,131 XPMΒ·at block #6,831,875 Β· updates every 60s
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