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Home/Chain Registry/Block #1,249,627

Block #1,249,627

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/23/2015, 12:56:16 PM Β· Difficulty 10.7676 Β· 5,577,352 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5f74e0d026cac0724f5026b1b4378cddc6f6642af0de9a27645cfdc3b4efd018
View on Chainz β†—

Difficulty

10.767598

Transactions

1

Size

199 B

Version

2

Bits

0ac48147

Nonce

1,388,303,404

Timestamp

9/23/2015, 12:56:16 PM

Confirmations

5,577,352

Merkle Root

2669829964c0773c4957b3b13fcef83e41d29c6106180478dd52ea6f3e9d92e6
Transactions (1)
Coinbase2669829964c077…52ea6f3e9d92e6
1 in β†’ 1 out8.6100 XPM109 B
AUAXzPJ8…n8UQmADR
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.

1.192 Γ— 10⁹⁡(96-digit number)
11923438578786261987…58218065012694001200
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
1.192 Γ— 10⁹⁡(96-digit number)
11923438578786261987…58218065012694001201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.384 Γ— 10⁹⁡(96-digit number)
23846877157572523974…16436130025388002401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.769 Γ— 10⁹⁡(96-digit number)
47693754315145047949…32872260050776004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.538 Γ— 10⁹⁡(96-digit number)
95387508630290095898…65744520101552009601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.907 Γ— 10⁹⁢(97-digit number)
19077501726058019179…31489040203104019201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.815 Γ— 10⁹⁢(97-digit number)
38155003452116038359…62978080406208038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.631 Γ— 10⁹⁢(97-digit number)
76310006904232076718…25956160812416076801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.526 Γ— 10⁹⁷(98-digit number)
15262001380846415343…51912321624832153601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.052 Γ— 10⁹⁷(98-digit number)
30524002761692830687…03824643249664307201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.104 Γ— 10⁹⁷(98-digit number)
61048005523385661374…07649286499328614401
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 1249627

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 5f74e0d026cac0724f5026b1b4378cddc6f6642af0de9a27645cfdc3b4efd018

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 #1,249,627 on Chainz β†—
Circulating Supply:57,860,006 XPMΒ·at block #6,826,978 Β· updates every 60s
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