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Home/Chain Registry/Block #2,129,301

Block #2,129,301

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/23/2017, 2:39:23 PM Β· Difficulty 10.9105 Β· 4,708,138 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1e0ee8a987b8e3964aac3f43f90c92408c742a26340cfa829d492c62eaa5c979
View on Chainz β†—

Difficulty

10.910518

Transactions

1

Size

200 B

Version

2

Bits

0ae917bb

Nonce

52,205,158

Timestamp

5/23/2017, 2:39:23 PM

Confirmations

4,708,138

Merkle Root

bdceaf22e3aaf93302b1c923bc1e280d4d5716fbef47bd59711d1f81bede6c70
Transactions (1)
Coinbasebdceaf22e3aaf9…1d1f81bede6c70
1 in β†’ 1 out8.3900 XPM109 B
ANRqJEZX…4SVyT5Fc
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.

1.465 Γ— 10⁹⁷(98-digit number)
14658188425356122597…45435593367807989760
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
1.465 Γ— 10⁹⁷(98-digit number)
14658188425356122597…45435593367807989759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.931 Γ— 10⁹⁷(98-digit number)
29316376850712245195…90871186735615979519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.863 Γ— 10⁹⁷(98-digit number)
58632753701424490390…81742373471231959039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.172 Γ— 10⁹⁸(99-digit number)
11726550740284898078…63484746942463918079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.345 Γ— 10⁹⁸(99-digit number)
23453101480569796156…26969493884927836159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.690 Γ— 10⁹⁸(99-digit number)
46906202961139592312…53938987769855672319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.381 Γ— 10⁹⁸(99-digit number)
93812405922279184624…07877975539711344639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.876 Γ— 10⁹⁹(100-digit number)
18762481184455836924…15755951079422689279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.752 Γ— 10⁹⁹(100-digit number)
37524962368911673849…31511902158845378559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.504 Γ— 10⁹⁹(100-digit number)
75049924737823347699…63023804317690757119
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 2129301

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 1e0ee8a987b8e3964aac3f43f90c92408c742a26340cfa829d492c62eaa5c979

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 #2,129,301 on Chainz β†—
Circulating Supply:57,943,834 XPMΒ·at block #6,837,438 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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