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Home/Chain Registry/Block #2,047,646

Block #2,047,646

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/1/2017, 4:59:04 AM Β· Difficulty 10.6875 Β· 4,791,996 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d245cfc361ab965e3fa0104be9b95e7ad58fb309332d9f59d6bd771f9b2a242e
View on Chainz β†—

Difficulty

10.687526

Transactions

2

Size

1016 B

Version

2

Bits

0ab001b9

Nonce

145,255,619

Timestamp

4/1/2017, 4:59:04 AM

Confirmations

4,791,996

Merkle Root

c4d4c525058934c433f7409e1fd717578a28c1a42953402dded4408bb907fcd6
Transactions (2)
Coinbase1331a553e57b84…80a5fcd7245fd5
1 in β†’ 1 out8.7500 XPM109 B
AYkNVea1…hKjKTHDU
8cafbb460338a9…d2347c8357b7c4
5 in β†’ 2 out791.2651 XPM817 B
AMG7SN4y…17H44PecAcFnNkyp…abCsvUgv
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.

2.184 Γ— 10⁹⁴(95-digit number)
21842143859681724417…51176376261786851000
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
2.184 Γ— 10⁹⁴(95-digit number)
21842143859681724417…51176376261786850999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.368 Γ— 10⁹⁴(95-digit number)
43684287719363448834…02352752523573701999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.736 Γ— 10⁹⁴(95-digit number)
87368575438726897669…04705505047147403999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.747 Γ— 10⁹⁡(96-digit number)
17473715087745379533…09411010094294807999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.494 Γ— 10⁹⁡(96-digit number)
34947430175490759067…18822020188589615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.989 Γ— 10⁹⁡(96-digit number)
69894860350981518135…37644040377179231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.397 Γ— 10⁹⁢(97-digit number)
13978972070196303627…75288080754358463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.795 Γ— 10⁹⁢(97-digit number)
27957944140392607254…50576161508716927999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.591 Γ— 10⁹⁢(97-digit number)
55915888280785214508…01152323017433855999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.118 Γ— 10⁹⁷(98-digit number)
11183177656157042901…02304646034867711999
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 2047646

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 d245cfc361ab965e3fa0104be9b95e7ad58fb309332d9f59d6bd771f9b2a242e

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 #2,047,646 on Chainz β†—
Circulating Supply:57,961,431 XPMΒ·at block #6,839,641 Β· updates every 60s
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