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Home/Chain Registry/Block #2,774,179

Block #2,774,179

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/1/2018, 3:42:12 AM Β· Difficulty 11.6648 Β· 4,066,179 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4008d30631d0b83bef1809954fe2889841eca226d227f60c27c9c2e0f0e0b02c
View on Chainz β†—

Difficulty

11.664838

Transactions

1

Size

198 B

Version

2

Bits

0baa32d0

Nonce

35,050,700

Timestamp

8/1/2018, 3:42:12 AM

Confirmations

4,066,179

Merkle Root

061c4a10453b96a861f1828134cde9fd3581ab0f6bf0648289d6ba7243b0a5e4
Transactions (1)
Coinbase061c4a10453b96…d6ba7243b0a5e4
1 in β†’ 1 out7.3400 XPM109 B
AbE6jhP7…sg3i7UG9
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.

2.546 Γ— 10⁹³(94-digit number)
25461722356738996917…58593761901522272960
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
2.546 Γ— 10⁹³(94-digit number)
25461722356738996917…58593761901522272961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.092 Γ— 10⁹³(94-digit number)
50923444713477993834…17187523803044545921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.018 Γ— 10⁹⁴(95-digit number)
10184688942695598766…34375047606089091841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.036 Γ— 10⁹⁴(95-digit number)
20369377885391197533…68750095212178183681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.073 Γ— 10⁹⁴(95-digit number)
40738755770782395067…37500190424356367361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.147 Γ— 10⁹⁴(95-digit number)
81477511541564790135…75000380848712734721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.629 Γ— 10⁹⁡(96-digit number)
16295502308312958027…50000761697425469441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.259 Γ— 10⁹⁡(96-digit number)
32591004616625916054…00001523394850938881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.518 Γ— 10⁹⁡(96-digit number)
65182009233251832108…00003046789701877761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.303 Γ— 10⁹⁢(97-digit number)
13036401846650366421…00006093579403755521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.607 Γ— 10⁹⁢(97-digit number)
26072803693300732843…00012187158807511041
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 2774179

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 4008d30631d0b83bef1809954fe2889841eca226d227f60c27c9c2e0f0e0b02c

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 #2,774,179 on Chainz β†—
Circulating Supply:57,967,180 XPMΒ·at block #6,840,357 Β· updates every 60s
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