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Block #645,028

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/23/2014, 6:07:15 PM Β· Difficulty 10.9541 Β· 6,154,974 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ccb48d85ab962ed038e138f83e5133594bdff5eb855b99f20a460a7b3a85af2c
View on Chainz β†—

Height

#645,028

Difficulty

10.954056

Transactions

3

Size

887 B

Version

2

Bits

0af43d08

Nonce

1,929,965,649

Timestamp

7/23/2014, 6:07:15 PM

Confirmations

6,154,974

Merkle Root

d25818e8ea0344d9a543fb695e2c46ded20a1807fed4bad453abba0896a1db0e
Transactions (3)
Coinbase4c5a9a6b3b7655…7276431c03d02d
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
3f9ac9fd9ee322…15b763a3eeac4f
1 in β†’ 2 out8.3100 XPM191 B
AHbqA1Lc…6FYig9qrAeKNrjNj…1NEq95Ta
199e7f896657b1…5f28f26f3b366d
3 in β†’ 1 out23.7020 XPM489 B
AXL1AJoL…xURwCSKe
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.

2.930 Γ— 10⁹⁢(97-digit number)
29300566360124867694…67956007651006736560
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
2.930 Γ— 10⁹⁢(97-digit number)
29300566360124867694…67956007651006736559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.860 Γ— 10⁹⁢(97-digit number)
58601132720249735389…35912015302013473119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.172 Γ— 10⁹⁷(98-digit number)
11720226544049947077…71824030604026946239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.344 Γ— 10⁹⁷(98-digit number)
23440453088099894155…43648061208053892479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.688 Γ— 10⁹⁷(98-digit number)
46880906176199788311…87296122416107784959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.376 Γ— 10⁹⁷(98-digit number)
93761812352399576623…74592244832215569919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.875 Γ— 10⁹⁸(99-digit number)
18752362470479915324…49184489664431139839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.750 Γ— 10⁹⁸(99-digit number)
37504724940959830649…98368979328862279679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.500 Γ— 10⁹⁸(99-digit number)
75009449881919661299…96737958657724559359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.500 Γ— 10⁹⁹(100-digit number)
15001889976383932259…93475917315449118719
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 645028

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 ccb48d85ab962ed038e138f83e5133594bdff5eb855b99f20a460a7b3a85af2c

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 #645,028 on Chainz β†—
Circulating Supply:57,644,072 XPMΒ·at block #6,800,001 Β· updates every 60s
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