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Home/Chain Registry/Block #2,098,745

Block #2,098,745

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2017, 9:13:41 PM Β· Difficulty 10.8616 Β· 4,733,103 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
22f071774ccf5bd6b8830d4b3c37547e7f0de2d03ef6dae191d126451dbcbc35
View on Chainz β†—

Difficulty

10.861587

Transactions

1

Size

199 B

Version

2

Bits

0adc90fb

Nonce

1,020,996,405

Timestamp

5/3/2017, 9:13:41 PM

Confirmations

4,733,103

Merkle Root

70a8f0cb9f1962a436d3466d465a318612ebae355a8e7f17013aeca54c10353f
Transactions (1)
Coinbase70a8f0cb9f1962…3aeca54c10353f
1 in β†’ 1 out8.4600 XPM109 B
AGM4Xts7…T57QgQwy
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.

1.878 Γ— 10⁹⁡(96-digit number)
18785688183619577756…14288453676845487680
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
1.878 Γ— 10⁹⁡(96-digit number)
18785688183619577756…14288453676845487681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.757 Γ— 10⁹⁡(96-digit number)
37571376367239155513…28576907353690975361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.514 Γ— 10⁹⁡(96-digit number)
75142752734478311027…57153814707381950721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.502 Γ— 10⁹⁢(97-digit number)
15028550546895662205…14307629414763901441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.005 Γ— 10⁹⁢(97-digit number)
30057101093791324410…28615258829527802881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.011 Γ— 10⁹⁢(97-digit number)
60114202187582648821…57230517659055605761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.202 Γ— 10⁹⁷(98-digit number)
12022840437516529764…14461035318111211521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.404 Γ— 10⁹⁷(98-digit number)
24045680875033059528…28922070636222423041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.809 Γ— 10⁹⁷(98-digit number)
48091361750066119057…57844141272444846081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.618 Γ— 10⁹⁷(98-digit number)
96182723500132238114…15688282544889692161
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 2098745

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 22f071774ccf5bd6b8830d4b3c37547e7f0de2d03ef6dae191d126451dbcbc35

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 #2,098,745 on Chainz β†—
Circulating Supply:57,898,905 XPMΒ·at block #6,831,847 Β· updates every 60s
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