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Home/Chain Registry/Block #2,072,261

Block #2,072,261

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/15/2017, 4:05:42 PM Β· Difficulty 10.8535 Β· 4,760,365 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ddfac69d83cb004692c2f0c2c44d3d8028d793a88e1e174b78eb38ccde7c158c
View on Chainz β†—

Difficulty

10.853458

Transactions

1

Size

209 B

Version

2

Bits

0ada7c3f

Nonce

114,223,329

Timestamp

4/15/2017, 4:05:42 PM

Confirmations

4,760,365

Merkle Root

f6290cd079f0c0b0ce53a133b666c662f2b21e66727c954693489f5df58caa74
Transactions (1)
Coinbasef6290cd079f0c0…489f5df58caa74
1 in β†’ 1 out8.4800 XPM118 B
AM6GYpjw…aw86QDtR
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.

1.097 Γ— 10⁹⁷(98-digit number)
10977036987922367865…50841642562486272000
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
1.097 Γ— 10⁹⁷(98-digit number)
10977036987922367865…50841642562486271999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.195 Γ— 10⁹⁷(98-digit number)
21954073975844735731…01683285124972543999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.390 Γ— 10⁹⁷(98-digit number)
43908147951689471463…03366570249945087999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.781 Γ— 10⁹⁷(98-digit number)
87816295903378942926…06733140499890175999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.756 Γ— 10⁹⁸(99-digit number)
17563259180675788585…13466280999780351999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.512 Γ— 10⁹⁸(99-digit number)
35126518361351577170…26932561999560703999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.025 Γ— 10⁹⁸(99-digit number)
70253036722703154341…53865123999121407999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.405 Γ— 10⁹⁹(100-digit number)
14050607344540630868…07730247998242815999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.810 Γ— 10⁹⁹(100-digit number)
28101214689081261736…15460495996485631999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.620 Γ— 10⁹⁹(100-digit number)
56202429378162523473…30920991992971263999
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 2072261

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 ddfac69d83cb004692c2f0c2c44d3d8028d793a88e1e174b78eb38ccde7c158c

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 #2,072,261 on Chainz β†—
Circulating Supply:57,905,156 XPMΒ·at block #6,832,625 Β· updates every 60s
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