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Home/Chain Registry/Block #2,169,977

Block #2,169,977

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/21/2017, 6:07:13 AM Β· Difficulty 10.9010 Β· 4,674,171 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
54a55d9da55f98045923b866d0ee3e64e264f7fac29c649361e8acfe783bbff7
View on Chainz β†—

Difficulty

10.901015

Transactions

1

Size

201 B

Version

2

Bits

0ae6a8e4

Nonce

461,056,656

Timestamp

6/21/2017, 6:07:13 AM

Confirmations

4,674,171

Merkle Root

a432e672d0fd21d562ecaa544af5e83ce0ceca5369fe9dbb8dbab79ced0ec198
Transactions (1)
Coinbasea432e672d0fd21…bab79ced0ec198
1 in β†’ 1 out8.4000 XPM110 B
AQkx1jqw…XvwAzr3d
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.

3.632 Γ— 10⁹⁢(97-digit number)
36320407576311740750…54294519037807861760
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
3.632 Γ— 10⁹⁢(97-digit number)
36320407576311740750…54294519037807861759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.264 Γ— 10⁹⁢(97-digit number)
72640815152623481501…08589038075615723519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.452 Γ— 10⁹⁷(98-digit number)
14528163030524696300…17178076151231447039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.905 Γ— 10⁹⁷(98-digit number)
29056326061049392600…34356152302462894079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.811 Γ— 10⁹⁷(98-digit number)
58112652122098785201…68712304604925788159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.162 Γ— 10⁹⁸(99-digit number)
11622530424419757040…37424609209851576319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.324 Γ— 10⁹⁸(99-digit number)
23245060848839514080…74849218419703152639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.649 Γ— 10⁹⁸(99-digit number)
46490121697679028161…49698436839406305279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.298 Γ— 10⁹⁸(99-digit number)
92980243395358056322…99396873678812610559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.859 Γ— 10⁹⁹(100-digit number)
18596048679071611264…98793747357625221119
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 2169977

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 54a55d9da55f98045923b866d0ee3e64e264f7fac29c649361e8acfe783bbff7

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 #2,169,977 on Chainz β†—
Circulating Supply:57,997,561 XPMΒ·at block #6,844,147 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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