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Block #672,061

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/10/2014, 4:34:24 PM Β· Difficulty 10.9645 Β· 6,172,410 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6173ebc68bbdfd1e0d33b9ec509a7785927b9912bf788706b37f8be53a01c07b
View on Chainz β†—

Height

#672,061

Difficulty

10.964523

Transactions

1

Size

206 B

Version

2

Bits

0af6eafd

Nonce

13,510,266

Timestamp

8/10/2014, 4:34:24 PM

Confirmations

6,172,410

Merkle Root

9b02f887385042a6d415534e32628c2fd4776db7e34b83609f48eef7f5f6a984
Transactions (1)
Coinbase9b02f887385042…48eef7f5f6a984
1 in β†’ 1 out8.3000 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.

1.063 Γ— 10⁹⁡(96-digit number)
10634062390665247851…70827962739315368160
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
1.063 Γ— 10⁹⁡(96-digit number)
10634062390665247851…70827962739315368161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.126 Γ— 10⁹⁡(96-digit number)
21268124781330495703…41655925478630736321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.253 Γ— 10⁹⁡(96-digit number)
42536249562660991406…83311850957261472641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.507 Γ— 10⁹⁡(96-digit number)
85072499125321982812…66623701914522945281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.701 Γ— 10⁹⁢(97-digit number)
17014499825064396562…33247403829045890561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.402 Γ— 10⁹⁢(97-digit number)
34028999650128793124…66494807658091781121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.805 Γ— 10⁹⁢(97-digit number)
68057999300257586249…32989615316183562241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.361 Γ— 10⁹⁷(98-digit number)
13611599860051517249…65979230632367124481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.722 Γ— 10⁹⁷(98-digit number)
27223199720103034499…31958461264734248961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.444 Γ— 10⁹⁷(98-digit number)
54446399440206068999…63916922529468497921
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 672061

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 6173ebc68bbdfd1e0d33b9ec509a7785927b9912bf788706b37f8be53a01c07b

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 #672,061 on Chainz β†—
Circulating Supply:58,000,163 XPMΒ·at block #6,844,470 Β· updates every 60s
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