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Block #2,212,236

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2017, 4:14:28 PM Β· Difficulty 10.9441 Β· 4,628,152 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b3ca6c0a000426d91c7b25ac8b6620ce37638be70490bbd1598a37d34b77cc3a
View on Chainz β†—

Difficulty

10.944150

Transactions

1

Size

199 B

Version

2

Bits

0af1b3cd

Nonce

1,177,122,955

Timestamp

7/18/2017, 4:14:28 PM

Confirmations

4,628,152

Merkle Root

be06ffb7aab8f7e52ca21edbf4dd898bce2058b4179ab8fa572f29aca1de8c7c
Transactions (1)
Coinbasebe06ffb7aab8f7…2f29aca1de8c7c
1 in β†’ 1 out8.3400 XPM109 B
ASHfbLA4…J59JcAQ3
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.

5.823 Γ— 10⁹⁴(95-digit number)
58235070309297364661…00531050002414630400
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
5.823 Γ— 10⁹⁴(95-digit number)
58235070309297364661…00531050002414630399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.164 Γ— 10⁹⁡(96-digit number)
11647014061859472932…01062100004829260799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.329 Γ— 10⁹⁡(96-digit number)
23294028123718945864…02124200009658521599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.658 Γ— 10⁹⁡(96-digit number)
46588056247437891729…04248400019317043199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.317 Γ— 10⁹⁡(96-digit number)
93176112494875783458…08496800038634086399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.863 Γ— 10⁹⁢(97-digit number)
18635222498975156691…16993600077268172799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.727 Γ— 10⁹⁢(97-digit number)
37270444997950313383…33987200154536345599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.454 Γ— 10⁹⁢(97-digit number)
74540889995900626766…67974400309072691199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.490 Γ— 10⁹⁷(98-digit number)
14908177999180125353…35948800618145382399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.981 Γ— 10⁹⁷(98-digit number)
29816355998360250706…71897601236290764799
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 2212236

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 b3ca6c0a000426d91c7b25ac8b6620ce37638be70490bbd1598a37d34b77cc3a

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 #2,212,236 on Chainz β†—
Circulating Supply:57,967,426 XPMΒ·at block #6,840,387 Β· updates every 60s
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