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Block #103,123

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2013, 10:57:42 AM Β· Difficulty 9.5158 Β· 6,697,144 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e3e310ea260563bd25f08d599997dfcaef65757e6a5970e8910b99201ab983d5
View on Chainz β†—

Height

#103,123

Difficulty

9.515787

Transactions

2

Size

392 B

Version

2

Bits

09840aa3

Nonce

62,250

Timestamp

8/7/2013, 10:57:42 AM

Confirmations

6,697,144

Merkle Root

b5331b77743f0a1521d180c22e08e1b80710fde6a6c4af320ab80a93b38abfde
Transactions (2)
Coinbaseeffbef894a489d…cad56441617ab6
1 in β†’ 1 out11.0400 XPM109 B
AYnPP6jG…Q3sS4Pbg
cbbf54370e506f…558f88389c371a
1 in β†’ 2 out11.7100 XPM192 B
AWRNfTvn…1UMbsd8nAUySZuZe…22spvY5T
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.

3.706 Γ— 10⁹⁢(97-digit number)
37068199599014605067…26164067335436677450
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
3.706 Γ— 10⁹⁢(97-digit number)
37068199599014605067…26164067335436677451
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.413 Γ— 10⁹⁢(97-digit number)
74136399198029210135…52328134670873354901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.482 Γ— 10⁹⁷(98-digit number)
14827279839605842027…04656269341746709801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.965 Γ— 10⁹⁷(98-digit number)
29654559679211684054…09312538683493419601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.930 Γ— 10⁹⁷(98-digit number)
59309119358423368108…18625077366986839201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.186 Γ— 10⁹⁸(99-digit number)
11861823871684673621…37250154733973678401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.372 Γ— 10⁹⁸(99-digit number)
23723647743369347243…74500309467947356801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.744 Γ— 10⁹⁸(99-digit number)
47447295486738694486…49000618935894713601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.489 Γ— 10⁹⁸(99-digit number)
94894590973477388973…98001237871789427201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 103123

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 e3e310ea260563bd25f08d599997dfcaef65757e6a5970e8910b99201ab983d5

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 #103,123 on Chainz β†—
Circulating Supply:57,646,193 XPMΒ·at block #6,800,266 Β· updates every 60s
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