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Home/Chain Registry/Block #2,270,552

Block #2,270,552

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/27/2017, 4:45:42 PM Β· Difficulty 10.9529 Β· 4,563,232 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
23619f53074e3bcfa38d7fdce59184004217525a636dce074bb63302e06463b5
View on Chainz β†—

Difficulty

10.952909

Transactions

3

Size

1.90 KB

Version

2

Bits

0af3f1df

Nonce

75,292,195

Timestamp

8/27/2017, 4:45:42 PM

Confirmations

4,563,232

Merkle Root

54b9b4370e9b4d35e0234e7fd0ea8061a7475e0d805b5bf36b0facb6202ccee6
Transactions (3)
Coinbasece4c33aae55d19…ac2595703c5b5e
1 in β†’ 1 out8.3600 XPM110 B
AbLZHdfw…uSutssSt
175d1baabd68fb…d00b101f0620d1
2 in β†’ 1 out990.0000 XPM340 B
ATcbvWF6…7XYUkWNR
bd3fa94e15d5c9…0bd9c859f0065c
9 in β†’ 2 out2970.0192 XPM1.38 KB
AR8t12ra…pgP11W6RAcF9KL3M…x8o1RuUz
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.

2.257 Γ— 10⁹⁷(98-digit number)
22571246874132461932…02951526775433246720
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
2.257 Γ— 10⁹⁷(98-digit number)
22571246874132461932…02951526775433246721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.514 Γ— 10⁹⁷(98-digit number)
45142493748264923864…05903053550866493441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.028 Γ— 10⁹⁷(98-digit number)
90284987496529847728…11806107101732986881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.805 Γ— 10⁹⁸(99-digit number)
18056997499305969545…23612214203465973761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.611 Γ— 10⁹⁸(99-digit number)
36113994998611939091…47224428406931947521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.222 Γ— 10⁹⁸(99-digit number)
72227989997223878182…94448856813863895041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.444 Γ— 10⁹⁹(100-digit number)
14445597999444775636…88897713627727790081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.889 Γ— 10⁹⁹(100-digit number)
28891195998889551273…77795427255455580161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.778 Γ— 10⁹⁹(100-digit number)
57782391997779102546…55590854510911160321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.155 Γ— 10¹⁰⁰(101-digit number)
11556478399555820509…11181709021822320641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.311 Γ— 10¹⁰⁰(101-digit number)
23112956799111641018…22363418043644641281
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 2270552

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 23619f53074e3bcfa38d7fdce59184004217525a636dce074bb63302e06463b5

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 #2,270,552 on Chainz β†—
Circulating Supply:57,914,492 XPMΒ·at block #6,833,783 Β· updates every 60s
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