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Home/Chain Registry/Block #3,276,902

Block #3,276,902

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/22/2019, 10:33:08 AM Β· Difficulty 10.9950 Β· 3,565,954 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b35ca6826fb51120cd136069f60bdcc4a1e11a69e3f9bd440d7e1b17145e7695
View on Chainz β†—

Difficulty

10.995031

Transactions

1

Size

200 B

Version

2

Bits

0afeba58

Nonce

1,228,267,797

Timestamp

7/22/2019, 10:33:08 AM

Confirmations

3,565,954

Merkle Root

4434524b66d8260d6197e70a6a789f9a49cc92e7213913a660980e67b1d3dd1f
Transactions (1)
Coinbase4434524b66d826…980e67b1d3dd1f
1 in β†’ 1 out8.2600 XPM109 B
ASiq2qtK…VMhmk7yL
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.

4.044 Γ— 10⁹⁢(97-digit number)
40446603432580197571…72699767995971153920
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
4.044 Γ— 10⁹⁢(97-digit number)
40446603432580197571…72699767995971153919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.089 Γ— 10⁹⁢(97-digit number)
80893206865160395142…45399535991942307839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.617 Γ— 10⁹⁷(98-digit number)
16178641373032079028…90799071983884615679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.235 Γ— 10⁹⁷(98-digit number)
32357282746064158056…81598143967769231359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.471 Γ— 10⁹⁷(98-digit number)
64714565492128316113…63196287935538462719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.294 Γ— 10⁹⁸(99-digit number)
12942913098425663222…26392575871076925439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.588 Γ— 10⁹⁸(99-digit number)
25885826196851326445…52785151742153850879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.177 Γ— 10⁹⁸(99-digit number)
51771652393702652891…05570303484307701759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.035 Γ— 10⁹⁹(100-digit number)
10354330478740530578…11140606968615403519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.070 Γ— 10⁹⁹(100-digit number)
20708660957481061156…22281213937230807039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.141 Γ— 10⁹⁹(100-digit number)
41417321914962122312…44562427874461614079
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 3276902

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 b35ca6826fb51120cd136069f60bdcc4a1e11a69e3f9bd440d7e1b17145e7695

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 #3,276,902 on Chainz β†—
Circulating Supply:57,987,195 XPMΒ·at block #6,842,855 Β· updates every 60s
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