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Home/Chain Registry/Block #1,609,818

Block #1,609,818

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/1/2016, 4:10:14 PM Β· Difficulty 10.6123 Β· 5,223,653 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
04a7ea9aea52241ad72c09ee7321d9abce605f29d4fb1a452e59f1d177d7d8ee
View on Chainz β†—

Difficulty

10.612313

Transactions

1

Size

201 B

Version

2

Bits

0a9cc088

Nonce

763,811,881

Timestamp

6/1/2016, 4:10:14 PM

Confirmations

5,223,653

Merkle Root

1da2cab19c4138ba27d792817d6a347546d5d2b7e07c596dacb90f87ea8ccfce
Transactions (1)
Coinbase1da2cab19c4138…b90f87ea8ccfce
1 in β†’ 1 out8.8700 XPM110 B
AGkQNH66…dmouXr2U
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.

2.739 Γ— 10⁹⁢(97-digit number)
27391968229067544631…76060349193109519360
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
2.739 Γ— 10⁹⁢(97-digit number)
27391968229067544631…76060349193109519361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.478 Γ— 10⁹⁢(97-digit number)
54783936458135089263…52120698386219038721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.095 Γ— 10⁹⁷(98-digit number)
10956787291627017852…04241396772438077441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.191 Γ— 10⁹⁷(98-digit number)
21913574583254035705…08482793544876154881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.382 Γ— 10⁹⁷(98-digit number)
43827149166508071410…16965587089752309761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.765 Γ— 10⁹⁷(98-digit number)
87654298333016142821…33931174179504619521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.753 Γ— 10⁹⁸(99-digit number)
17530859666603228564…67862348359009239041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.506 Γ— 10⁹⁸(99-digit number)
35061719333206457128…35724696718018478081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.012 Γ— 10⁹⁸(99-digit number)
70123438666412914257…71449393436036956161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.402 Γ— 10⁹⁹(100-digit number)
14024687733282582851…42898786872073912321
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 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
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 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 1609818

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 04a7ea9aea52241ad72c09ee7321d9abce605f29d4fb1a452e59f1d177d7d8ee

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 #1,609,818 on Chainz β†—
Circulating Supply:57,911,970 XPMΒ·at block #6,833,470 Β· updates every 60s
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