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Home/Chain Registry/Block #2,090,060

Block #2,090,060

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/27/2017, 11:16:54 AM Β· Difficulty 10.8757 Β· 4,751,430 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
57c2a67346c74ada719c5c83beef034b245365850da43d13aa6bcd6a9f52ac90
View on Chainz β†—

Difficulty

10.875715

Transactions

3

Size

1.15 KB

Version

2

Bits

0ae02ee0

Nonce

1,780,964,234

Timestamp

4/27/2017, 11:16:54 AM

Confirmations

4,751,430

Merkle Root

446ba05c1632d01eb6a98a173d8ea54ceb095260c8d7e03dcc1f1dd7abba6041
Transactions (3)
Coinbase5727176b77a084…d9bfc71b247345
1 in β†’ 1 out8.4600 XPM109 B
ANA67Qsr…x1zP6ouH
9d5ee1d49e2cc7…c60351ae84867d
5 in β†’ 1 out1018.2700 XPM785 B
AKc8GdcV…PFmVnxov
ac9f2f657c8f65…845b11b3ca4735
1 in β†’ 1 out0.0670 XPM193 B
AUh6zJjq…yMn5wt6U
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.

1.510 Γ— 10⁹⁴(95-digit number)
15103585729035795528…21193797043403009210
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
1.510 Γ— 10⁹⁴(95-digit number)
15103585729035795528…21193797043403009211
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.020 Γ— 10⁹⁴(95-digit number)
30207171458071591057…42387594086806018421
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.041 Γ— 10⁹⁴(95-digit number)
60414342916143182115…84775188173612036841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.208 Γ— 10⁹⁡(96-digit number)
12082868583228636423…69550376347224073681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.416 Γ— 10⁹⁡(96-digit number)
24165737166457272846…39100752694448147361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.833 Γ— 10⁹⁡(96-digit number)
48331474332914545692…78201505388896294721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.666 Γ— 10⁹⁡(96-digit number)
96662948665829091384…56403010777792589441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.933 Γ— 10⁹⁢(97-digit number)
19332589733165818276…12806021555585178881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.866 Γ— 10⁹⁢(97-digit number)
38665179466331636553…25612043111170357761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.733 Γ— 10⁹⁢(97-digit number)
77330358932663273107…51224086222340715521
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 2090060

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 57c2a67346c74ada719c5c83beef034b245365850da43d13aa6bcd6a9f52ac90

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 #2,090,060 on Chainz β†—
Circulating Supply:57,976,296 XPMΒ·at block #6,841,489 Β· updates every 60s
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