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Block #850,802

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/12/2014, 7:32:44 PM Β· Difficulty 10.9710 Β· 5,991,557 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3cb33f633cb9f38893cf4922c186764ab4a03e4ca3d88cc8a72fade929bb2c40
View on Chainz β†—

Height

#850,802

Difficulty

10.971036

Transactions

3

Size

623 B

Version

2

Bits

0af895d2

Nonce

2,400,020,217

Timestamp

12/12/2014, 7:32:44 PM

Confirmations

5,991,557

Merkle Root

2bd68c25f9c6922c3907882e3c90387290a0c15fb7b866b79b2f363612718dd2
Transactions (3)
Coinbase0a3cdf5e0129e0…c9abbed931be60
1 in β†’ 1 out8.3290 XPM116 B
ANSXnLY2…Sd25TjkD
4766f7ae250795…80d546a082f378
1 in β†’ 1 out0.0116 XPM191 B
AXfZ5oC4…Ki6vVRwK
801d0170bc9f7a…9f97d222e844dc
1 in β†’ 2 out0.0210 XPM226 B
AaMiqL3S…WWKDadFEAL4kvgbm…YbTVDXxw
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.

9.038 Γ— 10⁹⁴(95-digit number)
90388847791410004162…26102985098240162080
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
9.038 Γ— 10⁹⁴(95-digit number)
90388847791410004162…26102985098240162079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.807 Γ— 10⁹⁡(96-digit number)
18077769558282000832…52205970196480324159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.615 Γ— 10⁹⁡(96-digit number)
36155539116564001664…04411940392960648319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.231 Γ— 10⁹⁡(96-digit number)
72311078233128003329…08823880785921296639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.446 Γ— 10⁹⁢(97-digit number)
14462215646625600665…17647761571842593279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.892 Γ— 10⁹⁢(97-digit number)
28924431293251201331…35295523143685186559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.784 Γ— 10⁹⁢(97-digit number)
57848862586502402663…70591046287370373119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.156 Γ— 10⁹⁷(98-digit number)
11569772517300480532…41182092574740746239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.313 Γ— 10⁹⁷(98-digit number)
23139545034600961065…82364185149481492479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.627 Γ— 10⁹⁷(98-digit number)
46279090069201922130…64728370298962984959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.255 Γ— 10⁹⁷(98-digit number)
92558180138403844261…29456740597925969919
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 850802

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 3cb33f633cb9f38893cf4922c186764ab4a03e4ca3d88cc8a72fade929bb2c40

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 #850,802 on Chainz β†—
Circulating Supply:57,983,279 XPMΒ·at block #6,842,358 Β· updates every 60s
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