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Home/Chain Registry/Block #2,261,854

Block #2,261,854

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/21/2017, 4:55:59 PM Β· Difficulty 10.9520 Β· 4,581,673 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
abd6c32a50a08787ac76300e02cb2943786b2c454ba9af72ecd7b18432af726c
View on Chainz β†—

Difficulty

10.951983

Transactions

1

Size

200 B

Version

2

Bits

0af3b528

Nonce

1,561,672,632

Timestamp

8/21/2017, 4:55:59 PM

Confirmations

4,581,673

Merkle Root

f3e9a92e9cf3f7b5b3c988de20c4d0c6f3b2ffe11286da31766776675decb08d
Transactions (1)
Coinbasef3e9a92e9cf3f7…6776675decb08d
1 in β†’ 1 out8.3200 XPM110 B
AP4chsKt…JmYXSNGg
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.

4.749 Γ— 10⁹⁴(95-digit number)
47497255415199796986…64942067676211041120
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
4.749 Γ— 10⁹⁴(95-digit number)
47497255415199796986…64942067676211041119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.499 Γ— 10⁹⁴(95-digit number)
94994510830399593972…29884135352422082239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.899 Γ— 10⁹⁡(96-digit number)
18998902166079918794…59768270704844164479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.799 Γ— 10⁹⁡(96-digit number)
37997804332159837589…19536541409688328959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.599 Γ— 10⁹⁡(96-digit number)
75995608664319675178…39073082819376657919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.519 Γ— 10⁹⁢(97-digit number)
15199121732863935035…78146165638753315839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.039 Γ— 10⁹⁢(97-digit number)
30398243465727870071…56292331277506631679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.079 Γ— 10⁹⁢(97-digit number)
60796486931455740142…12584662555013263359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.215 Γ— 10⁹⁷(98-digit number)
12159297386291148028…25169325110026526719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.431 Γ— 10⁹⁷(98-digit number)
24318594772582296057…50338650220053053439
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 2261854

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 abd6c32a50a08787ac76300e02cb2943786b2c454ba9af72ecd7b18432af726c

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 #2,261,854 on Chainz β†—
Circulating Supply:57,992,593 XPMΒ·at block #6,843,526 Β· updates every 60s
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