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Home/Chain Registry/Block #2,730,049

Block #2,730,049

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/1/2018, 8:18:44 PM Β· Difficulty 11.6291 Β· 4,101,692 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1498651b4dcbcbe942e434d2cf9eacbc56411b372998544e6ad1df3d0e85dcf4
View on Chainz β†—

Difficulty

11.629132

Transactions

2

Size

723 B

Version

2

Bits

0ba10ece

Nonce

1,477,273,733

Timestamp

7/1/2018, 8:18:44 PM

Confirmations

4,101,692

Merkle Root

8e9acc7d895388f3b81f41c26cdddc093a8f0c07be07a2c99cd30ecd951cd24c
Transactions (2)
Coinbaseba7039691fc44d…ef96c2c5abb0c2
1 in β†’ 1 out7.3900 XPM110 B
AdppB2Mm…cAfGrAqC
adb36f0a9cd4a6…d41bfd31c53b0d
3 in β†’ 2 out894.0104 XPM523 B
ARY67Yio…VS88Q8ouANEKqHH9…p3ucaGtj
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.

7.260 Γ— 10⁹³(94-digit number)
72600211978781478171…29558947802229635920
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
7.260 Γ— 10⁹³(94-digit number)
72600211978781478171…29558947802229635919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.452 Γ— 10⁹⁴(95-digit number)
14520042395756295634…59117895604459271839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.904 Γ— 10⁹⁴(95-digit number)
29040084791512591268…18235791208918543679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.808 Γ— 10⁹⁴(95-digit number)
58080169583025182537…36471582417837087359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.161 Γ— 10⁹⁡(96-digit number)
11616033916605036507…72943164835674174719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.323 Γ— 10⁹⁡(96-digit number)
23232067833210073014…45886329671348349439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.646 Γ— 10⁹⁡(96-digit number)
46464135666420146029…91772659342696698879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.292 Γ— 10⁹⁡(96-digit number)
92928271332840292059…83545318685393397759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.858 Γ— 10⁹⁢(97-digit number)
18585654266568058411…67090637370786795519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.717 Γ— 10⁹⁢(97-digit number)
37171308533136116823…34181274741573591039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.434 Γ— 10⁹⁢(97-digit number)
74342617066272233647…68362549483147182079
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 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
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 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 2730049

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 1498651b4dcbcbe942e434d2cf9eacbc56411b372998544e6ad1df3d0e85dcf4

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 #2,730,049 on Chainz β†—
Circulating Supply:57,898,034 XPMΒ·at block #6,831,740 Β· updates every 60s
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