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Block #1,611,418

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/2/2016, 7:58:10 PM Β· Difficulty 10.6069 Β· 5,229,886 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3699f0116aecd41b969fd3470d392f633e061dd602500674f36ca6326aa54ee5
View on Chainz β†—

Difficulty

10.606897

Transactions

1

Size

200 B

Version

2

Bits

0a9b5d97

Nonce

1,119,596,971

Timestamp

6/2/2016, 7:58:10 PM

Confirmations

5,229,886

Merkle Root

578986bbc83d9aea390452a62eca5d40e2fc0c91fc8c264738b84518acd09e04
Transactions (1)
Coinbase578986bbc83d9a…b84518acd09e04
1 in β†’ 1 out8.8700 XPM109 B
AXFRjVxo…kov5vAN5
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.

8.540 Γ— 10⁹⁢(97-digit number)
85401767617034444242…57394707145249423360
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
8.540 Γ— 10⁹⁢(97-digit number)
85401767617034444242…57394707145249423361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.708 Γ— 10⁹⁷(98-digit number)
17080353523406888848…14789414290498846721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.416 Γ— 10⁹⁷(98-digit number)
34160707046813777696…29578828580997693441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.832 Γ— 10⁹⁷(98-digit number)
68321414093627555393…59157657161995386881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.366 Γ— 10⁹⁸(99-digit number)
13664282818725511078…18315314323990773761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.732 Γ— 10⁹⁸(99-digit number)
27328565637451022157…36630628647981547521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.465 Γ— 10⁹⁸(99-digit number)
54657131274902044315…73261257295963095041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.093 Γ— 10⁹⁹(100-digit number)
10931426254980408863…46522514591926190081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.186 Γ— 10⁹⁹(100-digit number)
21862852509960817726…93045029183852380161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.372 Γ— 10⁹⁹(100-digit number)
43725705019921635452…86090058367704760321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.745 Γ— 10⁹⁹(100-digit number)
87451410039843270904…72180116735409520641
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 1611418

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 3699f0116aecd41b969fd3470d392f633e061dd602500674f36ca6326aa54ee5

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 #1,611,418 on Chainz β†—
Circulating Supply:57,974,792 XPMΒ·at block #6,841,303 Β· updates every 60s
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