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Home/Chain Registry/Block #1,600,706

Block #1,600,706

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2016, 11:04:06 AM Β· Difficulty 10.5989 Β· 5,213,556 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d26737121565e2e5325ba9aa8c844c2b5f43c0ac4e6e99dbbbe73f25f62c9a44
View on Chainz β†—

Difficulty

10.598867

Transactions

1

Size

199 B

Version

2

Bits

0a994f61

Nonce

98,450,372

Timestamp

5/26/2016, 11:04:06 AM

Confirmations

5,213,556

Merkle Root

ced3d0d704088304cc56c982365b1e5dc2c014fb1f0593cb59bc32309b324071
Transactions (1)
Coinbaseced3d0d7040883…bc32309b324071
1 in β†’ 1 out8.8900 XPM109 B
AYudBRn1…4bELPMHW
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.

2.950 Γ— 10⁹⁡(96-digit number)
29503165690575045061…01623045735310777440
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
2.950 Γ— 10⁹⁡(96-digit number)
29503165690575045061…01623045735310777441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.900 Γ— 10⁹⁡(96-digit number)
59006331381150090123…03246091470621554881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.180 Γ— 10⁹⁢(97-digit number)
11801266276230018024…06492182941243109761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.360 Γ— 10⁹⁢(97-digit number)
23602532552460036049…12984365882486219521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.720 Γ— 10⁹⁢(97-digit number)
47205065104920072098…25968731764972439041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.441 Γ— 10⁹⁢(97-digit number)
94410130209840144196…51937463529944878081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.888 Γ— 10⁹⁷(98-digit number)
18882026041968028839…03874927059889756161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.776 Γ— 10⁹⁷(98-digit number)
37764052083936057678…07749854119779512321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.552 Γ— 10⁹⁷(98-digit number)
75528104167872115357…15499708239559024641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.510 Γ— 10⁹⁸(99-digit number)
15105620833574423071…30999416479118049281
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 1600706

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 d26737121565e2e5325ba9aa8c844c2b5f43c0ac4e6e99dbbbe73f25f62c9a44

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 #1,600,706 on Chainz β†—
Circulating Supply:57,758,163 XPMΒ·at block #6,814,261 Β· updates every 60s
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