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Block #196,456

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/6/2013, 12:12:43 PM Β· Difficulty 9.8809 Β· 6,598,569 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7a696fcdca84f248cc37a13dc6177c8a20d30cdbcfa46916dbd204d83fe9d657
View on Chainz β†—

Height

#196,456

Difficulty

9.880919

Transactions

1

Size

200 B

Version

2

Bits

09e183eb

Nonce

32,963

Timestamp

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

Confirmations

6,598,569

Merkle Root

290dd1979d1cbdaab9a8a7383c6f0b2b523eb09779cc3d8df4d3c4cb428fbe1f
Transactions (1)
Coinbase290dd1979d1cbd…d3c4cb428fbe1f
1 in β†’ 1 out10.2300 XPM109 B
ASUtGRx8…vh2tTKJs
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.

7.277 Γ— 10⁹⁷(98-digit number)
72775539299772927445…15295522346911728640
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
7.277 Γ— 10⁹⁷(98-digit number)
72775539299772927445…15295522346911728639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.455 Γ— 10⁹⁸(99-digit number)
14555107859954585489…30591044693823457279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.911 Γ— 10⁹⁸(99-digit number)
29110215719909170978…61182089387646914559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.822 Γ— 10⁹⁸(99-digit number)
58220431439818341956…22364178775293829119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.164 Γ— 10⁹⁹(100-digit number)
11644086287963668391…44728357550587658239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.328 Γ— 10⁹⁹(100-digit number)
23288172575927336782…89456715101175316479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.657 Γ— 10⁹⁹(100-digit number)
46576345151854673565…78913430202350632959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.315 Γ— 10⁹⁹(100-digit number)
93152690303709347130…57826860404701265919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.863 Γ— 10¹⁰⁰(101-digit number)
18630538060741869426…15653720809402531839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 196456

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 7a696fcdca84f248cc37a13dc6177c8a20d30cdbcfa46916dbd204d83fe9d657

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 #196,456 on Chainz β†—
Circulating Supply:57,604,247 XPMΒ·at block #6,795,024 Β· updates every 60s
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