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Home/Chain Registry/Block #2,275,335

Block #2,275,335

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/30/2017, 9:05:03 PM Β· Difficulty 10.9549 Β· 4,562,017 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
02e1f073644780e968141a5f440a97299021b3958291d20321d5315a01ee7760
View on Chainz β†—

Difficulty

10.954892

Transactions

1

Size

201 B

Version

2

Bits

0af473cf

Nonce

245,631,333

Timestamp

8/30/2017, 9:05:03 PM

Confirmations

4,562,017

Merkle Root

ea71952e4b088fb55bc056475beee8342b519461257321a2bc57dc79bd7a114c
Transactions (1)
Coinbaseea71952e4b088f…57dc79bd7a114c
1 in β†’ 1 out8.3200 XPM110 B
AXJ6EpBw…yHJuroyJ
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.

9.036 Γ— 10⁹⁢(97-digit number)
90364693861271891801…86238580409917825280
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
9.036 Γ— 10⁹⁢(97-digit number)
90364693861271891801…86238580409917825281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.807 Γ— 10⁹⁷(98-digit number)
18072938772254378360…72477160819835650561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.614 Γ— 10⁹⁷(98-digit number)
36145877544508756720…44954321639671301121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.229 Γ— 10⁹⁷(98-digit number)
72291755089017513441…89908643279342602241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.445 Γ— 10⁹⁸(99-digit number)
14458351017803502688…79817286558685204481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.891 Γ— 10⁹⁸(99-digit number)
28916702035607005376…59634573117370408961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.783 Γ— 10⁹⁸(99-digit number)
57833404071214010753…19269146234740817921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.156 Γ— 10⁹⁹(100-digit number)
11566680814242802150…38538292469481635841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.313 Γ— 10⁹⁹(100-digit number)
23133361628485604301…77076584938963271681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.626 Γ— 10⁹⁹(100-digit number)
46266723256971208602…54153169877926543361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.253 Γ— 10⁹⁹(100-digit number)
92533446513942417204…08306339755853086721
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2275335

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 02e1f073644780e968141a5f440a97299021b3958291d20321d5315a01ee7760

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 #2,275,335 on Chainz β†—
Circulating Supply:57,943,140 XPMΒ·at block #6,837,351 Β· updates every 60s
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