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Home/Chain Registry/Block #1,537,202

Block #1,537,202

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/12/2016, 1:03:46 AM Β· Difficulty 10.6306 Β· 5,306,147 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f808f19f49b5782ffd4d6be54e9802eb7780e6452fc8e7fdeb239ef552e921cb
View on Chainz β†—

Difficulty

10.630628

Transactions

1

Size

243 B

Version

2

Bits

0aa170d4

Nonce

755,770,006

Timestamp

4/12/2016, 1:03:46 AM

Confirmations

5,306,147

Merkle Root

f9a794949998a702d849896870e7831d6f4b1032d613f93c779cd5a2b55fdf7b
Transactions (1)
Coinbasef9a794949998a7…9cd5a2b55fdf7b
1 in β†’ 2 out8.8300 XPM152 B
AMsn7DGd…c6hoq7UkAXbk7f7A…Tx7JECPG
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.

7.147 Γ— 10⁹⁢(97-digit number)
71473132405476478041…87523667760507366400
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
7.147 Γ— 10⁹⁢(97-digit number)
71473132405476478041…87523667760507366401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.429 Γ— 10⁹⁷(98-digit number)
14294626481095295608…75047335521014732801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.858 Γ— 10⁹⁷(98-digit number)
28589252962190591216…50094671042029465601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.717 Γ— 10⁹⁷(98-digit number)
57178505924381182432…00189342084058931201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.143 Γ— 10⁹⁸(99-digit number)
11435701184876236486…00378684168117862401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.287 Γ— 10⁹⁸(99-digit number)
22871402369752472973…00757368336235724801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.574 Γ— 10⁹⁸(99-digit number)
45742804739504945946…01514736672471449601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.148 Γ— 10⁹⁸(99-digit number)
91485609479009891892…03029473344942899201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.829 Γ— 10⁹⁹(100-digit number)
18297121895801978378…06058946689885798401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.659 Γ— 10⁹⁹(100-digit number)
36594243791603956757…12117893379771596801
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 1537202

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 f808f19f49b5782ffd4d6be54e9802eb7780e6452fc8e7fdeb239ef552e921cb

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 #1,537,202 on Chainz β†—
Circulating Supply:57,991,153 XPMΒ·at block #6,843,348 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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