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Home/Chain Registry/Block #1,698,215

Block #1,698,215

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/1/2016, 12:20:32 PM Β· Difficulty 10.6719 Β· 5,141,098 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fc2e1beb4ed51417aa0fb8e2811cf584ad90de630d76552229168206102e1d5e
View on Chainz β†—

Difficulty

10.671937

Transactions

2

Size

424 B

Version

2

Bits

0aac040a

Nonce

447,392,574

Timestamp

8/1/2016, 12:20:32 PM

Confirmations

5,141,098

Merkle Root

9b29818e4126c7bdc49463a7a4768786d09438f0ed8697f8568df2ea0997a414
Transactions (2)
Coinbaseb274057cef14ac…f5bbb6e7d894c8
1 in β†’ 1 out8.7800 XPM109 B
AGrGWhHu…8CuACzZe
89f2e72c516766…71c52fd2f5ccd8
1 in β†’ 2 out0.1253 XPM225 B
APRwPtox…qFiVnR4yAPhGEjD2…1BYLqmyU
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.

3.038 Γ— 10⁹⁴(95-digit number)
30386052829283256913…88816224950994401920
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
3.038 Γ— 10⁹⁴(95-digit number)
30386052829283256913…88816224950994401919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.077 Γ— 10⁹⁴(95-digit number)
60772105658566513827…77632449901988803839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.215 Γ— 10⁹⁡(96-digit number)
12154421131713302765…55264899803977607679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.430 Γ— 10⁹⁡(96-digit number)
24308842263426605531…10529799607955215359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.861 Γ— 10⁹⁡(96-digit number)
48617684526853211062…21059599215910430719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.723 Γ— 10⁹⁡(96-digit number)
97235369053706422124…42119198431820861439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.944 Γ— 10⁹⁢(97-digit number)
19447073810741284424…84238396863641722879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.889 Γ— 10⁹⁢(97-digit number)
38894147621482568849…68476793727283445759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.778 Γ— 10⁹⁢(97-digit number)
77788295242965137699…36953587454566891519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.555 Γ— 10⁹⁷(98-digit number)
15557659048593027539…73907174909133783039
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 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
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 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 1698215

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 fc2e1beb4ed51417aa0fb8e2811cf584ad90de630d76552229168206102e1d5e

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 #1,698,215 on Chainz β†—
Circulating Supply:57,958,784 XPMΒ·at block #6,839,312 Β· updates every 60s
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