XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #39,640

Block #39,640

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 1:48:06 PM Β· Difficulty 8.3433 Β· 6,756,247 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
eb1cdcdb2ad007de999cfbdb4d143087ec4600cd35ed1e5562627e2ddd306550
View on Chainz β†—

Height

#39,640

Difficulty

8.343341

Transactions

2

Size

356 B

Version

2

Bits

0857e52f

Nonce

1,076

Timestamp

7/14/2013, 1:48:06 PM

Confirmations

6,756,247

Merkle Root

d06f4f14e7fa5859910ea803e30a662e11c0e0f0ee6c9fec245466f7dfa0838a
Transactions (2)
Coinbase611b7c15c53d55…23c693845a8b5b
1 in β†’ 1 out14.3600 XPM110 B
AXWphP8T…4trwmtBM
fabdefedf62dc2…b376b9461b5df5
1 in β†’ 1 out15.6100 XPM158 B
ANBXgfaf…ZXqNYSdt
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.

5.645 Γ— 10⁸⁹(90-digit number)
56455097734676355353…95066710850114798760
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
5.645 Γ— 10⁸⁹(90-digit number)
56455097734676355353…95066710850114798759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.129 Γ— 10⁹⁰(91-digit number)
11291019546935271070…90133421700229597519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.258 Γ— 10⁹⁰(91-digit number)
22582039093870542141…80266843400459195039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.516 Γ— 10⁹⁰(91-digit number)
45164078187741084282…60533686800918390079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.032 Γ— 10⁹⁰(91-digit number)
90328156375482168565…21067373601836780159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.806 Γ— 10⁹¹(92-digit number)
18065631275096433713…42134747203673560319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.613 Γ— 10⁹¹(92-digit number)
36131262550192867426…84269494407347120639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.226 Γ— 10⁹¹(92-digit number)
72262525100385734852…68538988814694241279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 39640

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 eb1cdcdb2ad007de999cfbdb4d143087ec4600cd35ed1e5562627e2ddd306550

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 #39,640 on Chainz β†—
Circulating Supply:57,611,179 XPMΒ·at block #6,795,886 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK