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Home/Chain Registry/Block #2,890,990

Block #2,890,990

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 10/21/2018, 7:09:34 PM Β· Difficulty 11.6153 Β· 3,953,116 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9e5d2974cae3b42088e37f03cbaf0dfb205bdf24d798d9ddea3469a5ddc632b5
View on Chainz β†—

Difficulty

11.615339

Transactions

1

Size

200 B

Version

2

Bits

0b9d86e3

Nonce

526,531,004

Timestamp

10/21/2018, 7:09:34 PM

Confirmations

3,953,116

Merkle Root

7203db74a4fe73870ba7cf1e3c0ee38c651a200dfc258523fa82278b9e2f372a
Transactions (1)
Coinbase7203db74a4fe73…82278b9e2f372a
1 in β†’ 1 out7.4000 XPM110 B
AGRAEmij…scFAjPN7
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.

9.132 Γ— 10⁹⁴(95-digit number)
91327136389079654462…60480255945938378200
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
9.132 Γ— 10⁹⁴(95-digit number)
91327136389079654462…60480255945938378199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.826 Γ— 10⁹⁡(96-digit number)
18265427277815930892…20960511891876756399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.653 Γ— 10⁹⁡(96-digit number)
36530854555631861785…41921023783753512799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.306 Γ— 10⁹⁡(96-digit number)
73061709111263723570…83842047567507025599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.461 Γ— 10⁹⁢(97-digit number)
14612341822252744714…67684095135014051199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.922 Γ— 10⁹⁢(97-digit number)
29224683644505489428…35368190270028102399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.844 Γ— 10⁹⁢(97-digit number)
58449367289010978856…70736380540056204799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.168 Γ— 10⁹⁷(98-digit number)
11689873457802195771…41472761080112409599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.337 Γ— 10⁹⁷(98-digit number)
23379746915604391542…82945522160224819199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.675 Γ— 10⁹⁷(98-digit number)
46759493831208783085…65891044320449638399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.351 Γ— 10⁹⁷(98-digit number)
93518987662417566170…31782088640899276799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.870 Γ— 10⁹⁸(99-digit number)
18703797532483513234…63564177281798553599
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 2890990

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 9e5d2974cae3b42088e37f03cbaf0dfb205bdf24d798d9ddea3469a5ddc632b5

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 #2,890,990 on Chainz β†—
Circulating Supply:57,997,221 XPMΒ·at block #6,844,105 Β· updates every 60s
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