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Home/Chain Registry/Block #2,610,764

Block #2,610,764

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/12/2018, 1:55:10 PM Β· Difficulty 11.2184 Β· 4,220,409 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0ea0d50d4063aeb7172efc37d988ebc46a654e35abb7845c59ea0dc03cee6498
View on Chainz β†—

Difficulty

11.218372

Transactions

1

Size

200 B

Version

2

Bits

0b37e73c

Nonce

1,590,426,102

Timestamp

4/12/2018, 1:55:10 PM

Confirmations

4,220,409

Merkle Root

cfdb3342a5e23b07fbad11e05e631946dbb2fe9eacfb0f4b9935a8b9d0b8aabd
Transactions (1)
Coinbasecfdb3342a5e23b…35a8b9d0b8aabd
1 in β†’ 1 out7.9300 XPM110 B
Adqah8zh…1WwoHJ9t
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.

4.630 Γ— 10⁹⁴(95-digit number)
46304072961812756503…08983180788964063200
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
4.630 Γ— 10⁹⁴(95-digit number)
46304072961812756503…08983180788964063199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.260 Γ— 10⁹⁴(95-digit number)
92608145923625513006…17966361577928126399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.852 Γ— 10⁹⁡(96-digit number)
18521629184725102601…35932723155856252799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.704 Γ— 10⁹⁡(96-digit number)
37043258369450205202…71865446311712505599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.408 Γ— 10⁹⁡(96-digit number)
74086516738900410404…43730892623425011199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.481 Γ— 10⁹⁢(97-digit number)
14817303347780082080…87461785246850022399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.963 Γ— 10⁹⁢(97-digit number)
29634606695560164161…74923570493700044799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.926 Γ— 10⁹⁢(97-digit number)
59269213391120328323…49847140987400089599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.185 Γ— 10⁹⁷(98-digit number)
11853842678224065664…99694281974800179199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.370 Γ— 10⁹⁷(98-digit number)
23707685356448131329…99388563949600358399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.741 Γ— 10⁹⁷(98-digit number)
47415370712896262659…98777127899200716799
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 2610764

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 0ea0d50d4063aeb7172efc37d988ebc46a654e35abb7845c59ea0dc03cee6498

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 #2,610,764 on Chainz β†—
Circulating Supply:57,893,525 XPMΒ·at block #6,831,172 Β· updates every 60s
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