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Home/Chain Registry/Block #1,016,012

Block #1,016,012

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/14/2015, 3:17:15 PM Β· Difficulty 10.7292 Β· 5,784,364 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2e6482a3f1e0232c65d102f88f21dc1d792894445bd32a1dd247efc09a7619b6
View on Chainz β†—

Difficulty

10.729187

Transactions

1

Size

207 B

Version

2

Bits

0abaac00

Nonce

321,185,847

Timestamp

4/14/2015, 3:17:15 PM

Confirmations

5,784,364

Merkle Root

0b0272c4c5d4b19fe1056f6f641b365a9a3e2dba6b9a4ac88156457c6b2a80a3
Transactions (1)
Coinbase0b0272c4c5d4b1…56457c6b2a80a3
1 in β†’ 1 out8.6700 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.630 Γ— 10⁹⁢(97-digit number)
16309183611514176285…49715307516260392960
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
1.630 Γ— 10⁹⁢(97-digit number)
16309183611514176285…49715307516260392959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.261 Γ— 10⁹⁢(97-digit number)
32618367223028352570…99430615032520785919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.523 Γ— 10⁹⁢(97-digit number)
65236734446056705141…98861230065041571839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.304 Γ— 10⁹⁷(98-digit number)
13047346889211341028…97722460130083143679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.609 Γ— 10⁹⁷(98-digit number)
26094693778422682056…95444920260166287359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.218 Γ— 10⁹⁷(98-digit number)
52189387556845364112…90889840520332574719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.043 Γ— 10⁹⁸(99-digit number)
10437877511369072822…81779681040665149439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.087 Γ— 10⁹⁸(99-digit number)
20875755022738145645…63559362081330298879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.175 Γ— 10⁹⁸(99-digit number)
41751510045476291290…27118724162660597759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.350 Γ— 10⁹⁸(99-digit number)
83503020090952582580…54237448325321195519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.670 Γ— 10⁹⁹(100-digit number)
16700604018190516516…08474896650642391039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 1016012

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 2e6482a3f1e0232c65d102f88f21dc1d792894445bd32a1dd247efc09a7619b6

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 #1,016,012 on Chainz β†—
Circulating Supply:57,647,067 XPMΒ·at block #6,800,375 Β· updates every 60s
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