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Block #760,767

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/10/2014, 4:44:22 PM Β· Difficulty 10.9725 Β· 6,063,745 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
09f4c7ebfd95fc3f1eadb949bbcf6b244b9f750ed78dc3379013992f0430666c
View on Chainz β†—

Height

#760,767

Difficulty

10.972453

Transactions

1

Size

207 B

Version

2

Bits

0af8f2b0

Nonce

489,716,188

Timestamp

10/10/2014, 4:44:22 PM

Confirmations

6,063,745

Merkle Root

75a1033850f665f34a45dfa3ee6a73da0f37fbaf899beff81a9f3fcc5a781d44
Transactions (1)
Coinbase75a1033850f665…9f3fcc5a781d44
1 in β†’ 1 out8.2900 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.

1.613 Γ— 10⁹⁢(97-digit number)
16135164497809699195…53832212670341658080
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
1.613 Γ— 10⁹⁢(97-digit number)
16135164497809699195…53832212670341658081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.227 Γ— 10⁹⁢(97-digit number)
32270328995619398390…07664425340683316161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.454 Γ— 10⁹⁢(97-digit number)
64540657991238796780…15328850681366632321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.290 Γ— 10⁹⁷(98-digit number)
12908131598247759356…30657701362733264641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.581 Γ— 10⁹⁷(98-digit number)
25816263196495518712…61315402725466529281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.163 Γ— 10⁹⁷(98-digit number)
51632526392991037424…22630805450933058561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.032 Γ— 10⁹⁸(99-digit number)
10326505278598207484…45261610901866117121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.065 Γ— 10⁹⁸(99-digit number)
20653010557196414969…90523221803732234241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.130 Γ— 10⁹⁸(99-digit number)
41306021114392829939…81046443607464468481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.261 Γ— 10⁹⁸(99-digit number)
82612042228785659879…62092887214928936961
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 760767

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 09f4c7ebfd95fc3f1eadb949bbcf6b244b9f750ed78dc3379013992f0430666c

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 #760,767 on Chainz β†—
Circulating Supply:57,840,157 XPMΒ·at block #6,824,511 Β· updates every 60s
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