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Home/Chain Registry/Block #2,157,246

Block #2,157,246

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/12/2017, 5:20:22 AM Β· Difficulty 10.9059 Β· 4,687,746 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f2ec5102c404c5a45ad11bd05bd4ecdc2dceecb9405433c562c28635bf90e86c
View on Chainz β†—

Difficulty

10.905919

Transactions

1

Size

200 B

Version

2

Bits

0ae7ea53

Nonce

727,737,357

Timestamp

6/12/2017, 5:20:22 AM

Confirmations

4,687,746

Merkle Root

1a02b7c8655c53da0bf7d85caf2c6a6283b1e9f8779bcf0421c0582ad0627061
Transactions (1)
Coinbase1a02b7c8655c53…c0582ad0627061
1 in β†’ 1 out8.3900 XPM110 B
AKkR6MY2…NX3wm6M6
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.

5.813 Γ— 10⁹³(94-digit number)
58132778820170172767…76247588550548947760
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
5.813 Γ— 10⁹³(94-digit number)
58132778820170172767…76247588550548947761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.162 Γ— 10⁹⁴(95-digit number)
11626555764034034553…52495177101097895521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.325 Γ— 10⁹⁴(95-digit number)
23253111528068069106…04990354202195791041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.650 Γ— 10⁹⁴(95-digit number)
46506223056136138213…09980708404391582081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.301 Γ— 10⁹⁴(95-digit number)
93012446112272276427…19961416808783164161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.860 Γ— 10⁹⁡(96-digit number)
18602489222454455285…39922833617566328321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.720 Γ— 10⁹⁡(96-digit number)
37204978444908910571…79845667235132656641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.440 Γ— 10⁹⁡(96-digit number)
74409956889817821142…59691334470265313281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.488 Γ— 10⁹⁢(97-digit number)
14881991377963564228…19382668940530626561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.976 Γ— 10⁹⁢(97-digit number)
29763982755927128456…38765337881061253121
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 2157246

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 f2ec5102c404c5a45ad11bd05bd4ecdc2dceecb9405433c562c28635bf90e86c

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 #2,157,246 on Chainz β†—
Circulating Supply:58,004,356 XPMΒ·at block #6,844,991 Β· updates every 60s
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