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Home/Chain Registry/Block #2,977,883

Block #2,977,883

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/23/2018, 7:51:24 AM Β· Difficulty 11.2859 Β· 3,865,981 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
00bdd84616830cdb25521ecc860507a80fc04a7311069bc7d89cad19334d66ed
View on Chainz β†—

Difficulty

11.285947

Transactions

1

Size

200 B

Version

2

Bits

0b4933d1

Nonce

864,817,300

Timestamp

12/23/2018, 7:51:24 AM

Confirmations

3,865,981

Merkle Root

742b786225bae57f5adf641bdb6910c72c459bc537327af144d95cf4764d42c8
Transactions (1)
Coinbase742b786225bae5…d95cf4764d42c8
1 in β†’ 1 out7.8400 XPM109 B
AUhjokok…k5m93PZR
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.

1.307 Γ— 10⁹⁢(97-digit number)
13077493918384087996…86311566092239708160
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.307 Γ— 10⁹⁢(97-digit number)
13077493918384087996…86311566092239708161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.615 Γ— 10⁹⁢(97-digit number)
26154987836768175992…72623132184479416321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.230 Γ— 10⁹⁢(97-digit number)
52309975673536351984…45246264368958832641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.046 Γ— 10⁹⁷(98-digit number)
10461995134707270396…90492528737917665281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.092 Γ— 10⁹⁷(98-digit number)
20923990269414540793…80985057475835330561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.184 Γ— 10⁹⁷(98-digit number)
41847980538829081587…61970114951670661121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.369 Γ— 10⁹⁷(98-digit number)
83695961077658163175…23940229903341322241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.673 Γ— 10⁹⁸(99-digit number)
16739192215531632635…47880459806682644481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.347 Γ— 10⁹⁸(99-digit number)
33478384431063265270…95760919613365288961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.695 Γ— 10⁹⁸(99-digit number)
66956768862126530540…91521839226730577921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.339 Γ— 10⁹⁹(100-digit number)
13391353772425306108…83043678453461155841
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2977883

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 00bdd84616830cdb25521ecc860507a80fc04a7311069bc7d89cad19334d66ed

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 #2,977,883 on Chainz β†—
Circulating Supply:57,995,281 XPMΒ·at block #6,843,863 Β· updates every 60s
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