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Home/Chain Registry/Block #2,070,742

Block #2,070,742

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/14/2017, 11:10:26 AM Β· Difficulty 10.8596 Β· 4,772,122 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
28fc701bdfdb41c09099a8ebd40cabb458ac1d4d98d5ba471565114f4d3ed76a
View on Chainz β†—

Difficulty

10.859559

Transactions

1

Size

201 B

Version

2

Bits

0adc0c0f

Nonce

2,129,568,407

Timestamp

4/14/2017, 11:10:26 AM

Confirmations

4,772,122

Merkle Root

b7cf491868531973a85075bb59a0a85a00ca51b9eb2b1ad1e353e0e8ada8a8c1
Transactions (1)
Coinbaseb7cf4918685319…53e0e8ada8a8c1
1 in β†’ 1 out8.4700 XPM110 B
AJd7DXq5…5eGy48Un
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.

9.679 Γ— 10⁹⁡(96-digit number)
96791980918833157844…46747617667476976640
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
9.679 Γ— 10⁹⁡(96-digit number)
96791980918833157844…46747617667476976639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.935 Γ— 10⁹⁢(97-digit number)
19358396183766631568…93495235334953953279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.871 Γ— 10⁹⁢(97-digit number)
38716792367533263137…86990470669907906559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.743 Γ— 10⁹⁢(97-digit number)
77433584735066526275…73980941339815813119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.548 Γ— 10⁹⁷(98-digit number)
15486716947013305255…47961882679631626239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.097 Γ— 10⁹⁷(98-digit number)
30973433894026610510…95923765359263252479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.194 Γ— 10⁹⁷(98-digit number)
61946867788053221020…91847530718526504959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.238 Γ— 10⁹⁸(99-digit number)
12389373557610644204…83695061437053009919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.477 Γ— 10⁹⁸(99-digit number)
24778747115221288408…67390122874106019839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.955 Γ— 10⁹⁸(99-digit number)
49557494230442576816…34780245748212039679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2070742

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 28fc701bdfdb41c09099a8ebd40cabb458ac1d4d98d5ba471565114f4d3ed76a

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 #2,070,742 on Chainz β†—
Circulating Supply:57,987,258 XPMΒ·at block #6,842,863 Β· updates every 60s
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