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Block #2,622,660

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/20/2018, 7:25:17 PM Β· Difficulty 11.2260 Β· 4,211,140 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
07d5377e1c152d654a7bccf89f95ca8986c63b2a79e0acdd5a40d24f6a8205e5
View on Chainz β†—

Difficulty

11.225978

Transactions

2

Size

574 B

Version

2

Bits

0b39d9b9

Nonce

1,321,767,391

Timestamp

4/20/2018, 7:25:17 PM

Confirmations

4,211,140

Merkle Root

e4364c08142b6e525baf881cc405b4e2f570a7ff318733fa0f7b4e9f4aa1a595
Transactions (2)
Coinbase769567e8a90f67…c078a7e1071a5d
1 in β†’ 1 out7.9300 XPM109 B
ALQGpaT6…9dLVU1B9
951c15903b3225…60f629206f9acc
2 in β†’ 2 out11.5300 XPM375 B
AXXGfizT…aeWx1CuiAMK2j3yb…yPL2heL1
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.

1.863 Γ— 10⁹⁡(96-digit number)
18634593919950905829…90446853170589135360
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
1.863 Γ— 10⁹⁡(96-digit number)
18634593919950905829…90446853170589135359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.726 Γ— 10⁹⁡(96-digit number)
37269187839901811659…80893706341178270719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.453 Γ— 10⁹⁡(96-digit number)
74538375679803623319…61787412682356541439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.490 Γ— 10⁹⁢(97-digit number)
14907675135960724663…23574825364713082879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.981 Γ— 10⁹⁢(97-digit number)
29815350271921449327…47149650729426165759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.963 Γ— 10⁹⁢(97-digit number)
59630700543842898655…94299301458852331519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.192 Γ— 10⁹⁷(98-digit number)
11926140108768579731…88598602917704663039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.385 Γ— 10⁹⁷(98-digit number)
23852280217537159462…77197205835409326079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.770 Γ— 10⁹⁷(98-digit number)
47704560435074318924…54394411670818652159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.540 Γ— 10⁹⁷(98-digit number)
95409120870148637848…08788823341637304319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.908 Γ— 10⁹⁸(99-digit number)
19081824174029727569…17577646683274608639
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 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
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 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 2622660

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 07d5377e1c152d654a7bccf89f95ca8986c63b2a79e0acdd5a40d24f6a8205e5

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 #2,622,660 on Chainz β†—
Circulating Supply:57,914,622 XPMΒ·at block #6,833,799 Β· updates every 60s
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