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Home/Chain Registry/Block #1,571,981

Block #1,571,981

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/5/2016, 2:04:21 AM Β· Difficulty 10.7322 Β· 5,269,810 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
09f23db2eec888dc578302cf7279d7d2fdfbbed307a7abac2bb0a6333f2d2a4d
View on Chainz β†—

Difficulty

10.732243

Transactions

1

Size

199 B

Version

2

Bits

0abb7445

Nonce

2,089,768,050

Timestamp

5/5/2016, 2:04:21 AM

Confirmations

5,269,810

Merkle Root

ba23fd57942e4a45afab29354d023e3aca944dd407fc06b46956cebe4733f393
Transactions (1)
Coinbaseba23fd57942e4a…56cebe4733f393
1 in β†’ 1 out8.6700 XPM109 B
AWjo1cY4…V4AiU3SF
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.

1.212 Γ— 10⁹⁴(95-digit number)
12122071540071170557…83743888637094461440
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
1.212 Γ— 10⁹⁴(95-digit number)
12122071540071170557…83743888637094461439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.424 Γ— 10⁹⁴(95-digit number)
24244143080142341114…67487777274188922879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.848 Γ— 10⁹⁴(95-digit number)
48488286160284682228…34975554548377845759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.697 Γ— 10⁹⁴(95-digit number)
96976572320569364457…69951109096755691519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.939 Γ— 10⁹⁡(96-digit number)
19395314464113872891…39902218193511383039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.879 Γ— 10⁹⁡(96-digit number)
38790628928227745782…79804436387022766079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.758 Γ— 10⁹⁡(96-digit number)
77581257856455491565…59608872774045532159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.551 Γ— 10⁹⁢(97-digit number)
15516251571291098313…19217745548091064319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.103 Γ— 10⁹⁢(97-digit number)
31032503142582196626…38435491096182128639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.206 Γ— 10⁹⁢(97-digit number)
62065006285164393252…76870982192364257279
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 1571981

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 09f23db2eec888dc578302cf7279d7d2fdfbbed307a7abac2bb0a6333f2d2a4d

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 #1,571,981 on Chainz β†—
Circulating Supply:57,978,706 XPMΒ·at block #6,841,790 Β· updates every 60s
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