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Home/Chain Registry/Block #1,102,686

Block #1,102,686

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/13/2015, 12:08:10 PM Β· Difficulty 10.7558 Β· 5,694,600 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
31b1e63f6b598d2324caf05fad292219413e3c129e8d25b8318d6842cced5dc9
View on Chainz β†—

Difficulty

10.755836

Transactions

1

Size

199 B

Version

2

Bits

0ac17e79

Nonce

310,373,466

Timestamp

6/13/2015, 12:08:10 PM

Confirmations

5,694,600

Merkle Root

69416c98172394e207d732d1fe6c5f0eefe4b631bc69c709e8add4fcbdcfd7d4
Transactions (1)
Coinbase69416c98172394…add4fcbdcfd7d4
1 in β†’ 1 out8.6300 XPM110 B
AXe7cqKk…giqZhSk3
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.

2.985 Γ— 10⁹³(94-digit number)
29859709456104283951…42699558061884844320
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
2.985 Γ— 10⁹³(94-digit number)
29859709456104283951…42699558061884844319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.971 Γ— 10⁹³(94-digit number)
59719418912208567902…85399116123769688639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.194 Γ— 10⁹⁴(95-digit number)
11943883782441713580…70798232247539377279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.388 Γ— 10⁹⁴(95-digit number)
23887767564883427161…41596464495078754559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.777 Γ— 10⁹⁴(95-digit number)
47775535129766854322…83192928990157509119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.555 Γ— 10⁹⁴(95-digit number)
95551070259533708644…66385857980315018239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.911 Γ— 10⁹⁡(96-digit number)
19110214051906741728…32771715960630036479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.822 Γ— 10⁹⁡(96-digit number)
38220428103813483457…65543431921260072959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.644 Γ— 10⁹⁡(96-digit number)
76440856207626966915…31086863842520145919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.528 Γ— 10⁹⁢(97-digit number)
15288171241525393383…62173727685040291839
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 1102686

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 31b1e63f6b598d2324caf05fad292219413e3c129e8d25b8318d6842cced5dc9

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 #1,102,686 on Chainz β†—
Circulating Supply:57,622,317 XPMΒ·at block #6,797,285 Β· updates every 60s
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