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Home/Chain Registry/Block #2,034,870

Block #2,034,870

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/23/2017, 9:19:19 AM Β· Difficulty 10.6806 Β· 4,806,834 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1a2985d60029c2b1d983b5205f21bccc0f2c4306010810aa8ca4dd96932be6d1
View on Chainz β†—

Difficulty

10.680590

Transactions

1

Size

200 B

Version

2

Bits

0aae3b1e

Nonce

120,342,127

Timestamp

3/23/2017, 9:19:19 AM

Confirmations

4,806,834

Merkle Root

7c5a51e8378eb8cf507c7f32b2c04545e16c001a942fb7b89e7e758679839c18
Transactions (1)
Coinbase7c5a51e8378eb8…7e758679839c18
1 in β†’ 1 out8.7500 XPM109 B
AN51cqEJ…gCNKoi9H
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.

1.464 Γ— 10⁹⁢(97-digit number)
14641543074188798967…85763302718744202240
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
1.464 Γ— 10⁹⁢(97-digit number)
14641543074188798967…85763302718744202239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.928 Γ— 10⁹⁢(97-digit number)
29283086148377597935…71526605437488404479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.856 Γ— 10⁹⁢(97-digit number)
58566172296755195871…43053210874976808959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.171 Γ— 10⁹⁷(98-digit number)
11713234459351039174…86106421749953617919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.342 Γ— 10⁹⁷(98-digit number)
23426468918702078348…72212843499907235839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.685 Γ— 10⁹⁷(98-digit number)
46852937837404156697…44425686999814471679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.370 Γ— 10⁹⁷(98-digit number)
93705875674808313394…88851373999628943359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.874 Γ— 10⁹⁸(99-digit number)
18741175134961662678…77702747999257886719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.748 Γ— 10⁹⁸(99-digit number)
37482350269923325357…55405495998515773439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.496 Γ— 10⁹⁸(99-digit number)
74964700539846650715…10810991997031546879
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 2034870

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 1a2985d60029c2b1d983b5205f21bccc0f2c4306010810aa8ca4dd96932be6d1

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 #2,034,870 on Chainz β†—
Circulating Supply:57,978,012 XPMΒ·at block #6,841,703 Β· updates every 60s
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