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Block #602,646

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/26/2014, 10:51:16 AM Β· Difficulty 10.9131 Β· 6,221,844 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cc2c19e0dd972f3d6a28e3571ae303104d41e35fcd680846e0a524c5a8a00523
View on Chainz β†—

Height

#602,646

Difficulty

10.913121

Transactions

1

Size

207 B

Version

2

Bits

0ae9c24e

Nonce

202,065,379

Timestamp

6/26/2014, 10:51:16 AM

Confirmations

6,221,844

Merkle Root

a97347769f92ed98aa1f4b9e11ef0ad5827964e499bd111a80cae3ef3b6f9422
Transactions (1)
Coinbasea97347769f92ed…cae3ef3b6f9422
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.891 Γ— 10⁹⁷(98-digit number)
18914122510994191069…41278304116240780160
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.891 Γ— 10⁹⁷(98-digit number)
18914122510994191069…41278304116240780161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.782 Γ— 10⁹⁷(98-digit number)
37828245021988382138…82556608232481560321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.565 Γ— 10⁹⁷(98-digit number)
75656490043976764277…65113216464963120641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.513 Γ— 10⁹⁸(99-digit number)
15131298008795352855…30226432929926241281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.026 Γ— 10⁹⁸(99-digit number)
30262596017590705711…60452865859852482561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.052 Γ— 10⁹⁸(99-digit number)
60525192035181411422…20905731719704965121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.210 Γ— 10⁹⁹(100-digit number)
12105038407036282284…41811463439409930241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.421 Γ— 10⁹⁹(100-digit number)
24210076814072564568…83622926878819860481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.842 Γ— 10⁹⁹(100-digit number)
48420153628145129137…67245853757639720961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.684 Γ— 10⁹⁹(100-digit number)
96840307256290258275…34491707515279441921
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 602646

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 cc2c19e0dd972f3d6a28e3571ae303104d41e35fcd680846e0a524c5a8a00523

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 #602,646 on Chainz β†—
Circulating Supply:57,839,991 XPMΒ·at block #6,824,489 Β· updates every 60s
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