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Home/Chain Registry/Block #2,097,901

Block #2,097,901

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2017, 2:30:21 AM Β· Difficulty 10.8691 Β· 4,729,026 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cfbbfda855bcc37686088458d5cf34dd69b2185fdb1bb614788aae23272ebad5
View on Chainz β†—

Difficulty

10.869078

Transactions

3

Size

42.45 KB

Version

2

Bits

0ade7be5

Nonce

1,659,327,436

Timestamp

5/3/2017, 2:30:21 AM

Confirmations

4,729,026

Merkle Root

d3e5e8950434bcb5c8b5e291c742be5a9d8951708dfbc1079470f0662542398b
Transactions (3)
Coinbase3f6335a37c22ea…6ba9da3e03d747
1 in β†’ 1 out8.9000 XPM109 B
AQ1YD1in…FJAyvTiB
8ce6d5b39ba079…ed06ea513b27ce
290 in β†’ 1 out36.0000 XPM41.93 KB
AVaj27ki…Ntfy4Rjn
8fc5616d067f58…60c352954958e7
2 in β†’ 1 out18.0000 XPM339 B
AVaj27ki…Ntfy4Rjn
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.

6.309 Γ— 10⁹²(93-digit number)
63094849649423986956…33834171642362645920
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
6.309 Γ— 10⁹²(93-digit number)
63094849649423986956…33834171642362645921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.261 Γ— 10⁹³(94-digit number)
12618969929884797391…67668343284725291841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.523 Γ— 10⁹³(94-digit number)
25237939859769594782…35336686569450583681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.047 Γ— 10⁹³(94-digit number)
50475879719539189564…70673373138901167361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.009 Γ— 10⁹⁴(95-digit number)
10095175943907837912…41346746277802334721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.019 Γ— 10⁹⁴(95-digit number)
20190351887815675825…82693492555604669441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.038 Γ— 10⁹⁴(95-digit number)
40380703775631351651…65386985111209338881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.076 Γ— 10⁹⁴(95-digit number)
80761407551262703303…30773970222418677761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.615 Γ— 10⁹⁡(96-digit number)
16152281510252540660…61547940444837355521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.230 Γ— 10⁹⁡(96-digit number)
32304563020505081321…23095880889674711041
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 2097901

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 cfbbfda855bcc37686088458d5cf34dd69b2185fdb1bb614788aae23272ebad5

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 #2,097,901 on Chainz β†—
Circulating Supply:57,859,587 XPMΒ·at block #6,826,926 Β· updates every 60s
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