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Home/Chain Registry/Block #163,965

Block #163,965

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 8:49:50 AM Β· Difficulty 9.8619 Β· 6,661,070 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
48fb818408a82b4dfb9c7d7ad9ee1d8cf32dafea059f127ceb80d7b606166d52
View on Chainz β†—

Height

#163,965

Difficulty

9.861879

Transactions

2

Size

572 B

Version

2

Bits

09dca417

Nonce

83,665

Timestamp

9/14/2013, 8:49:50 AM

Confirmations

6,661,070

Merkle Root

1006813fea6580ab77014686458caae86384523a194dd459b82cd9f4a22badbc
Transactions (2)
Coinbase9ad7ece218441c…0201ea54730d3a
1 in β†’ 1 out10.2800 XPM109 B
AYkoKAQ4…uuj8DeZs
bf7cff7d04daea…1385871aabf970
2 in β†’ 2 out1988.6900 XPM374 B
APZ2ne7t…3mPcpf4wAc2CiMxj…uF5QCCK8
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.

1.061 Γ— 10⁹²(93-digit number)
10617701248841470341…14999556910096752640
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
1.061 Γ— 10⁹²(93-digit number)
10617701248841470341…14999556910096752639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.123 Γ— 10⁹²(93-digit number)
21235402497682940682…29999113820193505279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.247 Γ— 10⁹²(93-digit number)
42470804995365881364…59998227640387010559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.494 Γ— 10⁹²(93-digit number)
84941609990731762728…19996455280774021119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.698 Γ— 10⁹³(94-digit number)
16988321998146352545…39992910561548042239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.397 Γ— 10⁹³(94-digit number)
33976643996292705091…79985821123096084479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.795 Γ— 10⁹³(94-digit number)
67953287992585410182…59971642246192168959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.359 Γ— 10⁹⁴(95-digit number)
13590657598517082036…19943284492384337919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.718 Γ— 10⁹⁴(95-digit number)
27181315197034164073…39886568984768675839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.436 Γ— 10⁹⁴(95-digit number)
54362630394068328146…79773137969537351679
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 163965

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 48fb818408a82b4dfb9c7d7ad9ee1d8cf32dafea059f127ceb80d7b606166d52

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 #163,965 on Chainz β†—
Circulating Supply:57,844,363 XPMΒ·at block #6,825,034 Β· updates every 60s
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