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Block #701,709

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/31/2014, 8:53:45 PM Β· Difficulty 10.9590 Β· 6,115,077 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
557503a4e67655704228e9ec977bbfeeb2d14512697f6c8c83e9c3bff9a74408
View on Chainz β†—

Height

#701,709

Difficulty

10.958991

Transactions

1

Size

207 B

Version

2

Bits

0af58071

Nonce

501,483,512

Timestamp

8/31/2014, 8:53:45 PM

Confirmations

6,115,077

Merkle Root

0fba79281953dca7aafa265d25141f901e14aa75fa16ab1f10524c8adb031d4d
Transactions (1)
Coinbase0fba79281953dc…524c8adb031d4d
1 in β†’ 1 out8.3100 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.

5.104 Γ— 10⁹⁷(98-digit number)
51048125149063020235…00963769046795537920
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
5.104 Γ— 10⁹⁷(98-digit number)
51048125149063020235…00963769046795537921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.020 Γ— 10⁹⁸(99-digit number)
10209625029812604047…01927538093591075841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.041 Γ— 10⁹⁸(99-digit number)
20419250059625208094…03855076187182151681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.083 Γ— 10⁹⁸(99-digit number)
40838500119250416188…07710152374364303361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.167 Γ— 10⁹⁸(99-digit number)
81677000238500832376…15420304748728606721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.633 Γ— 10⁹⁹(100-digit number)
16335400047700166475…30840609497457213441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.267 Γ— 10⁹⁹(100-digit number)
32670800095400332950…61681218994914426881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.534 Γ— 10⁹⁹(100-digit number)
65341600190800665900…23362437989828853761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.306 Γ— 10¹⁰⁰(101-digit number)
13068320038160133180…46724875979657707521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.613 Γ— 10¹⁰⁰(101-digit number)
26136640076320266360…93449751959315415041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.227 Γ— 10¹⁰⁰(101-digit number)
52273280152640532720…86899503918630830081
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 701709

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 557503a4e67655704228e9ec977bbfeeb2d14512697f6c8c83e9c3bff9a74408

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 #701,709 on Chainz β†—
Circulating Supply:57,778,323 XPMΒ·at block #6,816,785 Β· updates every 60s
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