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Block #1,873,590

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/1/2016, 10:22:49 AM Β· Difficulty 10.6681 Β· 4,963,830 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
52610d1795c28e373a3768e06999e83117319bcd9f7b4859d05655196d9298dc
View on Chainz β†—

Difficulty

10.668110

Transactions

1

Size

242 B

Version

2

Bits

0aab0949

Nonce

481,174,876

Timestamp

12/1/2016, 10:22:49 AM

Confirmations

4,963,830

Merkle Root

281eab11b66dd347b707f8c0f2dff481ea5b3f99940808fe56639ea4b16d41d0
Transactions (1)
Coinbase281eab11b66dd3…639ea4b16d41d0
1 in β†’ 2 out8.7700 XPM152 B
AYwHNztJ…6nxHXid1AXbk7f7A…Tx7JECPG
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.

5.954 Γ— 10⁹⁴(95-digit number)
59546166513317872619…96207570209620467200
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
5.954 Γ— 10⁹⁴(95-digit number)
59546166513317872619…96207570209620467199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.190 Γ— 10⁹⁡(96-digit number)
11909233302663574523…92415140419240934399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.381 Γ— 10⁹⁡(96-digit number)
23818466605327149047…84830280838481868799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.763 Γ— 10⁹⁡(96-digit number)
47636933210654298095…69660561676963737599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.527 Γ— 10⁹⁡(96-digit number)
95273866421308596191…39321123353927475199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.905 Γ— 10⁹⁢(97-digit number)
19054773284261719238…78642246707854950399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.810 Γ— 10⁹⁢(97-digit number)
38109546568523438476…57284493415709900799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.621 Γ— 10⁹⁢(97-digit number)
76219093137046876952…14568986831419801599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.524 Γ— 10⁹⁷(98-digit number)
15243818627409375390…29137973662839603199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.048 Γ— 10⁹⁷(98-digit number)
30487637254818750781…58275947325679206399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.097 Γ— 10⁹⁷(98-digit number)
60975274509637501562…16551894651358412799
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 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
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 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 1873590

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 52610d1795c28e373a3768e06999e83117319bcd9f7b4859d05655196d9298dc

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 #1,873,590 on Chainz β†—
Circulating Supply:57,943,680 XPMΒ·at block #6,837,419 Β· updates every 60s
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