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Block #163,963

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 8:47:05 AM Β· Difficulty 9.8619 Β· 6,660,558 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fc442fc72b57535f87f0a35f1d2928ef64be65834b6b529d0c4d9ee71c0addb8
View on Chainz β†—

Height

#163,963

Difficulty

9.861884

Transactions

1

Size

199 B

Version

2

Bits

09dca472

Nonce

84,109

Timestamp

9/14/2013, 8:47:05 AM

Confirmations

6,660,558

Merkle Root

a23f8b97d4ad477319893977e759f60a0f77966d98ebb0dde1ada0da66325453
Transactions (1)
Coinbasea23f8b97d4ad47…ada0da66325453
1 in β†’ 1 out10.2700 XPM109 B
AMjazV56…tVUuP32T
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.

4.153 Γ— 10⁹⁴(95-digit number)
41537697094543509339…82563468631126266880
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
4.153 Γ— 10⁹⁴(95-digit number)
41537697094543509339…82563468631126266879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.307 Γ— 10⁹⁴(95-digit number)
83075394189087018678…65126937262252533759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.661 Γ— 10⁹⁡(96-digit number)
16615078837817403735…30253874524505067519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.323 Γ— 10⁹⁡(96-digit number)
33230157675634807471…60507749049010135039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.646 Γ— 10⁹⁡(96-digit number)
66460315351269614943…21015498098020270079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.329 Γ— 10⁹⁢(97-digit number)
13292063070253922988…42030996196040540159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.658 Γ— 10⁹⁢(97-digit number)
26584126140507845977…84061992392081080319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.316 Γ— 10⁹⁢(97-digit number)
53168252281015691954…68123984784162160639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.063 Γ— 10⁹⁷(98-digit number)
10633650456203138390…36247969568324321279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 163963

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 fc442fc72b57535f87f0a35f1d2928ef64be65834b6b529d0c4d9ee71c0addb8

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 #163,963 on Chainz β†—
Circulating Supply:57,840,231 XPMΒ·at block #6,824,520 Β· updates every 60s
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