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Home/Chain Registry/Block #2,038,724

Block #2,038,724

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/26/2017, 1:34:24 AM Β· Difficulty 10.6806 Β· 4,802,082 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
17aced4ca4387508590c30d792536f0c2db81a3fdca91a820b98125eb52dcfce
View on Chainz β†—

Difficulty

10.680601

Transactions

1

Size

243 B

Version

2

Bits

0aae3bd9

Nonce

1,659,163,164

Timestamp

3/26/2017, 1:34:24 AM

Confirmations

4,802,082

Merkle Root

15a33ade45f6a4f939d1b762fa36558b13fd22325b2c18e29accab526784f35f
Transactions (1)
Coinbase15a33ade45f6a4…ccab526784f35f
1 in β†’ 2 out8.7500 XPM152 B
AavRL5n5…nfAScyPpALPu3s2c…EJXLjVFh
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.

9.222 Γ— 10⁹⁢(97-digit number)
92225364979501591922…05468982876799232000
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
9.222 Γ— 10⁹⁢(97-digit number)
92225364979501591922…05468982876799231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.844 Γ— 10⁹⁷(98-digit number)
18445072995900318384…10937965753598463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.689 Γ— 10⁹⁷(98-digit number)
36890145991800636768…21875931507196927999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.378 Γ— 10⁹⁷(98-digit number)
73780291983601273537…43751863014393855999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.475 Γ— 10⁹⁸(99-digit number)
14756058396720254707…87503726028787711999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.951 Γ— 10⁹⁸(99-digit number)
29512116793440509415…75007452057575423999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.902 Γ— 10⁹⁸(99-digit number)
59024233586881018830…50014904115150847999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.180 Γ— 10⁹⁹(100-digit number)
11804846717376203766…00029808230301695999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.360 Γ— 10⁹⁹(100-digit number)
23609693434752407532…00059616460603391999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.721 Γ— 10⁹⁹(100-digit number)
47219386869504815064…00119232921206783999
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 2038724

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 17aced4ca4387508590c30d792536f0c2db81a3fdca91a820b98125eb52dcfce

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 #2,038,724 on Chainz β†—
Circulating Supply:57,970,797 XPMΒ·at block #6,840,805 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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