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Home/Chain Registry/Block #3,076,370

Block #3,076,370

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/3/2019, 7:24:55 AM Β· Difficulty 11.0160 Β· 3,769,283 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
93f702b647ba9ee76d9e95b0e0ce900be430a6f8e89d87b73543312551693102
View on Chainz β†—

Difficulty

11.015990

Transactions

1

Size

200 B

Version

2

Bits

0b0417f4

Nonce

1,852,808,426

Timestamp

3/3/2019, 7:24:55 AM

Confirmations

3,769,283

Merkle Root

6ff6e21527dc2745b9e8385da7558b5c823841e0141393d44bbf3976eb5e51bc
Transactions (1)
Coinbase6ff6e21527dc27…bf3976eb5e51bc
1 in β†’ 1 out8.2300 XPM110 B
AUMQRepm…tAfKmdW1
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.

1.966 Γ— 10⁹⁡(96-digit number)
19669804576637348528…85204101045086287040
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
1.966 Γ— 10⁹⁡(96-digit number)
19669804576637348528…85204101045086287041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.933 Γ— 10⁹⁡(96-digit number)
39339609153274697056…70408202090172574081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.867 Γ— 10⁹⁡(96-digit number)
78679218306549394112…40816404180345148161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.573 Γ— 10⁹⁢(97-digit number)
15735843661309878822…81632808360690296321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.147 Γ— 10⁹⁢(97-digit number)
31471687322619757644…63265616721380592641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.294 Γ— 10⁹⁢(97-digit number)
62943374645239515289…26531233442761185281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.258 Γ— 10⁹⁷(98-digit number)
12588674929047903057…53062466885522370561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.517 Γ— 10⁹⁷(98-digit number)
25177349858095806115…06124933771044741121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.035 Γ— 10⁹⁷(98-digit number)
50354699716191612231…12249867542089482241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.007 Γ— 10⁹⁸(99-digit number)
10070939943238322446…24499735084178964481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.014 Γ— 10⁹⁸(99-digit number)
20141879886476644892…48999470168357928961
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 3076370

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 93f702b647ba9ee76d9e95b0e0ce900be430a6f8e89d87b73543312551693102

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 #3,076,370 on Chainz β†—
Circulating Supply:58,009,672 XPMΒ·at block #6,845,652 Β· updates every 60s
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