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Block #783,453

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/26/2014, 5:04:21 AM Β· Difficulty 10.9751 Β· 6,030,624 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
31d8f99d42c421fa41f2e1a268a50e2518c0bb583708a52b6d5109a5dd559b4e
View on Chainz β†—

Height

#783,453

Difficulty

10.975085

Transactions

1

Size

207 B

Version

2

Bits

0af99f26

Nonce

853,473,780

Timestamp

10/26/2014, 5:04:21 AM

Confirmations

6,030,624

Merkle Root

c9e91ee367a8c92c00740c7f27e8c9ca86ce405f014851e0b1e7ff7767de64f1
Transactions (1)
Coinbasec9e91ee367a8c9…e7ff7767de64f1
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.

2.898 Γ— 10⁹⁢(97-digit number)
28988466246567249160…52910843002208215040
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
2.898 Γ— 10⁹⁢(97-digit number)
28988466246567249160…52910843002208215041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.797 Γ— 10⁹⁢(97-digit number)
57976932493134498320…05821686004416430081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.159 Γ— 10⁹⁷(98-digit number)
11595386498626899664…11643372008832860161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.319 Γ— 10⁹⁷(98-digit number)
23190772997253799328…23286744017665720321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.638 Γ— 10⁹⁷(98-digit number)
46381545994507598656…46573488035331440641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.276 Γ— 10⁹⁷(98-digit number)
92763091989015197312…93146976070662881281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.855 Γ— 10⁹⁸(99-digit number)
18552618397803039462…86293952141325762561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.710 Γ— 10⁹⁸(99-digit number)
37105236795606078925…72587904282651525121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.421 Γ— 10⁹⁸(99-digit number)
74210473591212157850…45175808565303050241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.484 Γ— 10⁹⁹(100-digit number)
14842094718242431570…90351617130606100481
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 783453

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 31d8f99d42c421fa41f2e1a268a50e2518c0bb583708a52b6d5109a5dd559b4e

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 #783,453 on Chainz β†—
Circulating Supply:57,756,696 XPMΒ·at block #6,814,076 Β· updates every 60s
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