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Home/Chain Registry/Block #2,880,654

Block #2,880,654

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/14/2018, 11:04:34 AM Β· Difficulty 11.6321 Β· 3,961,419 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
37506eed4debff2c19207cd9d64f794838e5b1010624ed8c6420c6a700ae83f5
View on Chainz β†—

Difficulty

11.632082

Transactions

1

Size

200 B

Version

2

Bits

0ba1d01e

Nonce

431,262,742

Timestamp

10/14/2018, 11:04:34 AM

Confirmations

3,961,419

Merkle Root

48b91131483a1ce673b0510393c5d65e0a92a63bc82784513b1ba24a4453be04
Transactions (1)
Coinbase48b91131483a1c…1ba24a4453be04
1 in β†’ 1 out7.3800 XPM109 B
ALQGpaT6…9dLVU1B9
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.

3.823 Γ— 10⁹⁢(97-digit number)
38235549510015624533…32932417554238986240
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
3.823 Γ— 10⁹⁢(97-digit number)
38235549510015624533…32932417554238986239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.647 Γ— 10⁹⁢(97-digit number)
76471099020031249067…65864835108477972479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.529 Γ— 10⁹⁷(98-digit number)
15294219804006249813…31729670216955944959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.058 Γ— 10⁹⁷(98-digit number)
30588439608012499626…63459340433911889919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.117 Γ— 10⁹⁷(98-digit number)
61176879216024999253…26918680867823779839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.223 Γ— 10⁹⁸(99-digit number)
12235375843204999850…53837361735647559679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.447 Γ— 10⁹⁸(99-digit number)
24470751686409999701…07674723471295119359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.894 Γ— 10⁹⁸(99-digit number)
48941503372819999402…15349446942590238719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.788 Γ— 10⁹⁸(99-digit number)
97883006745639998805…30698893885180477439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.957 Γ— 10⁹⁹(100-digit number)
19576601349127999761…61397787770360954879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.915 Γ— 10⁹⁹(100-digit number)
39153202698255999522…22795575540721909759
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 2880654

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 37506eed4debff2c19207cd9d64f794838e5b1010624ed8c6420c6a700ae83f5

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 #2,880,654 on Chainz β†—
Circulating Supply:57,980,968 XPMΒ·at block #6,842,072 Β· updates every 60s
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