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Block #950,916

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/24/2015, 11:04:18 PM Β· Difficulty 10.8981 Β· 5,875,953 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5c5473fa356479bdb3a622b12214b53a2dd79d1e60c7b425304f6e00ce5f410e
View on Chainz β†—

Height

#950,916

Difficulty

10.898130

Transactions

1

Size

200 B

Version

2

Bits

0ae5ebd2

Nonce

1,682,736,677

Timestamp

2/24/2015, 11:04:18 PM

Confirmations

5,875,953

Merkle Root

4c4a52ae7f090d01f7027190ffc0d09ba6e5118b3e27e9d5a16ce206261abfe0
Transactions (1)
Coinbase4c4a52ae7f090d…6ce206261abfe0
1 in β†’ 1 out8.4100 XPM109 B
AUBTsdeH…Fuvc36hT
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.

1.131 Γ— 10⁹⁢(97-digit number)
11318687218515646841…59314464859999324160
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
1.131 Γ— 10⁹⁢(97-digit number)
11318687218515646841…59314464859999324161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.263 Γ— 10⁹⁢(97-digit number)
22637374437031293683…18628929719998648321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.527 Γ— 10⁹⁢(97-digit number)
45274748874062587367…37257859439997296641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.054 Γ— 10⁹⁢(97-digit number)
90549497748125174735…74515718879994593281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.810 Γ— 10⁹⁷(98-digit number)
18109899549625034947…49031437759989186561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.621 Γ— 10⁹⁷(98-digit number)
36219799099250069894…98062875519978373121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.243 Γ— 10⁹⁷(98-digit number)
72439598198500139788…96125751039956746241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.448 Γ— 10⁹⁸(99-digit number)
14487919639700027957…92251502079913492481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.897 Γ— 10⁹⁸(99-digit number)
28975839279400055915…84503004159826984961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.795 Γ— 10⁹⁸(99-digit number)
57951678558800111830…69006008319653969921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.159 Γ— 10⁹⁹(100-digit number)
11590335711760022366…38012016639307939841
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 950916

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 5c5473fa356479bdb3a622b12214b53a2dd79d1e60c7b425304f6e00ce5f410e

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 #950,916 on Chainz β†—
Circulating Supply:57,859,114 XPMΒ·at block #6,826,868 Β· updates every 60s
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