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Home/Chain Registry/Block #2,471,124

Block #2,471,124

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/13/2018, 1:26:00 PM Β· Difficulty 10.9617 Β· 4,371,122 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a81e0ed4d1dedca1048fab9162c875144cf363158abfbfdfe091bd6f49bc7965
View on Chainz β†—

Difficulty

10.961665

Transactions

1

Size

200 B

Version

2

Bits

0af62fa7

Nonce

1,902,723,605

Timestamp

1/13/2018, 1:26:00 PM

Confirmations

4,371,122

Merkle Root

c1e951897f18db759f3d87c3f11d0e994d92b06ea4e1677b7b09e259fe8bcd0e
Transactions (1)
Coinbasec1e951897f18db…09e259fe8bcd0e
1 in β†’ 1 out8.3100 XPM109 B
ALsh1wjn…RkKEMaNV
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.

1.585 Γ— 10⁹⁷(98-digit number)
15857584167441771671…11071097783441305600
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.585 Γ— 10⁹⁷(98-digit number)
15857584167441771671…11071097783441305601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.171 Γ— 10⁹⁷(98-digit number)
31715168334883543342…22142195566882611201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.343 Γ— 10⁹⁷(98-digit number)
63430336669767086684…44284391133765222401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.268 Γ— 10⁹⁸(99-digit number)
12686067333953417336…88568782267530444801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.537 Γ— 10⁹⁸(99-digit number)
25372134667906834673…77137564535060889601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.074 Γ— 10⁹⁸(99-digit number)
50744269335813669347…54275129070121779201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.014 Γ— 10⁹⁹(100-digit number)
10148853867162733869…08550258140243558401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.029 Γ— 10⁹⁹(100-digit number)
20297707734325467739…17100516280487116801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.059 Γ— 10⁹⁹(100-digit number)
40595415468650935478…34201032560974233601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.119 Γ— 10⁹⁹(100-digit number)
81190830937301870956…68402065121948467201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.623 Γ— 10¹⁰⁰(101-digit number)
16238166187460374191…36804130243896934401
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2471124

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 a81e0ed4d1dedca1048fab9162c875144cf363158abfbfdfe091bd6f49bc7965

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 #2,471,124 on Chainz β†—
Circulating Supply:57,982,366 XPMΒ·at block #6,842,245 Β· updates every 60s
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