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Block #207,988

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/13/2013, 6:12:43 PM Β· Difficulty 9.9048 Β· 6,592,318 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2b356e3fd9b823b3e491d0fadb41ea256498119444cd9918514fc412571e23ad
View on Chainz β†—

Height

#207,988

Difficulty

9.904845

Transactions

1

Size

204 B

Version

2

Bits

09e7a3f1

Nonce

16,778,487

Timestamp

10/13/2013, 6:12:43 PM

Confirmations

6,592,318

Merkle Root

49ee064f64900959a0b0589e2872c67a0714deb46ad6de37547ff54e1bd3eec9
Transactions (1)
Coinbase49ee064f649009…7ff54e1bd3eec9
1 in β†’ 1 out10.1800 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.925 Γ— 10⁹⁰(91-digit number)
19250880238182450170…30491226876101842160
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
1.925 Γ— 10⁹⁰(91-digit number)
19250880238182450170…30491226876101842159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.850 Γ— 10⁹⁰(91-digit number)
38501760476364900341…60982453752203684319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.700 Γ— 10⁹⁰(91-digit number)
77003520952729800682…21964907504407368639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.540 Γ— 10⁹¹(92-digit number)
15400704190545960136…43929815008814737279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.080 Γ— 10⁹¹(92-digit number)
30801408381091920272…87859630017629474559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.160 Γ— 10⁹¹(92-digit number)
61602816762183840545…75719260035258949119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.232 Γ— 10⁹²(93-digit number)
12320563352436768109…51438520070517898239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.464 Γ— 10⁹²(93-digit number)
24641126704873536218…02877040141035796479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.928 Γ— 10⁹²(93-digit number)
49282253409747072436…05754080282071592959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.856 Γ— 10⁹²(93-digit number)
98564506819494144873…11508160564143185919
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 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
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 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 207988

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 2b356e3fd9b823b3e491d0fadb41ea256498119444cd9918514fc412571e23ad

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 #207,988 on Chainz β†—
Circulating Supply:57,646,511 XPMΒ·at block #6,800,305 Β· updates every 60s
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