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Home/Chain Registry/Block #1,240,762

Block #1,240,762

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/17/2015, 1:14:56 PM Β· Difficulty 10.7558 Β· 5,602,010 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8bc734d26d83f587e8c038ef982fb2b1e0dd5a0a8d3a3b58bde5ed7ab4e4f358
View on Chainz β†—

Difficulty

10.755760

Transactions

1

Size

200 B

Version

2

Bits

0ac17980

Nonce

1,555,889,259

Timestamp

9/17/2015, 1:14:56 PM

Confirmations

5,602,010

Merkle Root

07e0c6674d9a085ecf15c5b48cd8d5d2f809b31809c815ccec25d406fa52c2c7
Transactions (1)
Coinbase07e0c6674d9a08…25d406fa52c2c7
1 in β†’ 1 out8.6300 XPM109 B
AUdC3mTK…WC5FsXnh
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.

1.004 Γ— 10⁹⁷(98-digit number)
10043971357362446039…40856972178649794560
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
1.004 Γ— 10⁹⁷(98-digit number)
10043971357362446039…40856972178649794561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.008 Γ— 10⁹⁷(98-digit number)
20087942714724892079…81713944357299589121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.017 Γ— 10⁹⁷(98-digit number)
40175885429449784159…63427888714599178241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.035 Γ— 10⁹⁷(98-digit number)
80351770858899568319…26855777429198356481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.607 Γ— 10⁹⁸(99-digit number)
16070354171779913663…53711554858396712961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.214 Γ— 10⁹⁸(99-digit number)
32140708343559827327…07423109716793425921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.428 Γ— 10⁹⁸(99-digit number)
64281416687119654655…14846219433586851841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.285 Γ— 10⁹⁹(100-digit number)
12856283337423930931…29692438867173703681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.571 Γ— 10⁹⁹(100-digit number)
25712566674847861862…59384877734347407361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.142 Γ— 10⁹⁹(100-digit number)
51425133349695723724…18769755468694814721
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 1240762

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 8bc734d26d83f587e8c038ef982fb2b1e0dd5a0a8d3a3b58bde5ed7ab4e4f358

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 #1,240,762 on Chainz β†—
Circulating Supply:57,986,514 XPMΒ·at block #6,842,771 Β· updates every 60s
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