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Block #686,212

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/21/2014, 11:22:35 AM Β· Difficulty 10.9540 Β· 6,130,405 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2cc79b3dd83df061926dd03a4e1242ebf1477dd73acd150e2d2aaec7f7f8438f
View on Chainz β†—

Height

#686,212

Difficulty

10.953992

Transactions

2

Size

728 B

Version

2

Bits

0af438d5

Nonce

160,121,328

Timestamp

8/21/2014, 11:22:35 AM

Confirmations

6,130,405

Merkle Root

abffeb6319664201361726e3044cdf67e6590c5134f7dad995fae8eee39f2aca
Transactions (2)
Coinbase56d318140dc396…812b1d82f15125
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
eb6db442cf4338…866b64a90cba33
3 in β†’ 2 out22.6634 XPM521 B
AZNi5r3u…sEWVLQxbAaU9J1Lk…4e47uLfq
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.

1.241 Γ— 10⁹⁸(99-digit number)
12419526284757394601…11026624833758686480
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
1.241 Γ— 10⁹⁸(99-digit number)
12419526284757394601…11026624833758686479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.483 Γ— 10⁹⁸(99-digit number)
24839052569514789203…22053249667517372959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.967 Γ— 10⁹⁸(99-digit number)
49678105139029578407…44106499335034745919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.935 Γ— 10⁹⁸(99-digit number)
99356210278059156814…88212998670069491839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.987 Γ— 10⁹⁹(100-digit number)
19871242055611831362…76425997340138983679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.974 Γ— 10⁹⁹(100-digit number)
39742484111223662725…52851994680277967359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.948 Γ— 10⁹⁹(100-digit number)
79484968222447325451…05703989360555934719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.589 Γ— 10¹⁰⁰(101-digit number)
15896993644489465090…11407978721111869439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.179 Γ— 10¹⁰⁰(101-digit number)
31793987288978930180…22815957442223738879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.358 Γ— 10¹⁰⁰(101-digit number)
63587974577957860361…45631914884447477759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.271 Γ— 10¹⁰¹(102-digit number)
12717594915591572072…91263829768894955519
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 686212

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 2cc79b3dd83df061926dd03a4e1242ebf1477dd73acd150e2d2aaec7f7f8438f

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 #686,212 on Chainz β†—
Circulating Supply:57,777,058 XPMΒ·at block #6,816,616 Β· updates every 60s
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