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Home/Chain Registry/Block #1,851,964

Block #1,851,964

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/16/2016, 6:05:48 PM Β· Difficulty 10.6333 Β· 4,974,647 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9859db89eba32ae53c3b9e86869d64f23a5f68209beb4efd8740a0faec51170f
View on Chainz β†—

Difficulty

10.633256

Transactions

1

Size

200 B

Version

2

Bits

0aa21d16

Nonce

824,332,329

Timestamp

11/16/2016, 6:05:48 PM

Confirmations

4,974,647

Merkle Root

f05f39e15a1c3fc116b0640e6421c0d45926991fc04ad830a1565fd121f03058
Transactions (1)
Coinbasef05f39e15a1c3f…565fd121f03058
1 in β†’ 1 out8.8300 XPM109 B
AaSgCi4E…y6EMQ5np
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.

1.203 Γ— 10⁹⁷(98-digit number)
12032760381614870221…65925592706623447040
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
1.203 Γ— 10⁹⁷(98-digit number)
12032760381614870221…65925592706623447039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.406 Γ— 10⁹⁷(98-digit number)
24065520763229740442…31851185413246894079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.813 Γ— 10⁹⁷(98-digit number)
48131041526459480884…63702370826493788159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.626 Γ— 10⁹⁷(98-digit number)
96262083052918961769…27404741652987576319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.925 Γ— 10⁹⁸(99-digit number)
19252416610583792353…54809483305975152639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.850 Γ— 10⁹⁸(99-digit number)
38504833221167584707…09618966611950305279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.700 Γ— 10⁹⁸(99-digit number)
77009666442335169415…19237933223900610559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.540 Γ— 10⁹⁹(100-digit number)
15401933288467033883…38475866447801221119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.080 Γ— 10⁹⁹(100-digit number)
30803866576934067766…76951732895602442239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.160 Γ— 10⁹⁹(100-digit number)
61607733153868135532…53903465791204884479
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 1851964

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 9859db89eba32ae53c3b9e86869d64f23a5f68209beb4efd8740a0faec51170f

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 #1,851,964 on Chainz β†—
Circulating Supply:57,857,040 XPMΒ·at block #6,826,610 Β· updates every 60s
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