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Home/Chain Registry/Block #2,690,267

Block #2,690,267

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/3/2018, 3:32:49 PM Β· Difficulty 11.6839 Β· 4,152,773 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cd310896f5d25f03db3ae16ea4fb91ab3b9a2f6bc9bbab9c4ecf037cac59f30c
View on Chainz β†—

Difficulty

11.683868

Transactions

1

Size

200 B

Version

2

Bits

0baf1201

Nonce

847,254,214

Timestamp

6/3/2018, 3:32:49 PM

Confirmations

4,152,773

Merkle Root

c163704e6af501d32fdfdcad14acab0b51555fafa33d3473ccca5a2ff9fb0b91
Transactions (1)
Coinbasec163704e6af501…ca5a2ff9fb0b91
1 in β†’ 1 out7.3100 XPM110 B
AXBGxpf3…pA5XGh5c
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.

3.977 Γ— 10⁹⁴(95-digit number)
39775294343850322461…65454020017840701440
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
3.977 Γ— 10⁹⁴(95-digit number)
39775294343850322461…65454020017840701441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.955 Γ— 10⁹⁴(95-digit number)
79550588687700644923…30908040035681402881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.591 Γ— 10⁹⁡(96-digit number)
15910117737540128984…61816080071362805761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.182 Γ— 10⁹⁡(96-digit number)
31820235475080257969…23632160142725611521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.364 Γ— 10⁹⁡(96-digit number)
63640470950160515938…47264320285451223041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.272 Γ— 10⁹⁢(97-digit number)
12728094190032103187…94528640570902446081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.545 Γ— 10⁹⁢(97-digit number)
25456188380064206375…89057281141804892161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.091 Γ— 10⁹⁢(97-digit number)
50912376760128412750…78114562283609784321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.018 Γ— 10⁹⁷(98-digit number)
10182475352025682550…56229124567219568641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.036 Γ— 10⁹⁷(98-digit number)
20364950704051365100…12458249134439137281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.072 Γ— 10⁹⁷(98-digit number)
40729901408102730200…24916498268878274561
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 2690267

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 cd310896f5d25f03db3ae16ea4fb91ab3b9a2f6bc9bbab9c4ecf037cac59f30c

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 #2,690,267 on Chainz β†—
Circulating Supply:57,988,677 XPMΒ·at block #6,843,039 Β· updates every 60s
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