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Block #103,610

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2013, 4:25:48 PM Β· Difficulty 9.5308 Β· 6,723,054 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
08eb83c4576ff698584d93d8437327b20b0e54f1ef85ca1ac1432639cbbe509d
View on Chainz β†—

Height

#103,610

Difficulty

9.530809

Transactions

1

Size

200 B

Version

2

Bits

0987e319

Nonce

71,968

Timestamp

8/7/2013, 4:25:48 PM

Confirmations

6,723,054

Merkle Root

3730ce50e87158f2762e3ecfa5b825028829d146b09ff9154ad78a4fffa4fcff
Transactions (1)
Coinbase3730ce50e87158…d78a4fffa4fcff
1 in β†’ 1 out10.9900 XPM109 B
AbcTDDcx…CeEjcBiP
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.

4.040 Γ— 10⁹⁢(97-digit number)
40402710532308396949…90493358176755665440
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
4.040 Γ— 10⁹⁢(97-digit number)
40402710532308396949…90493358176755665439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.080 Γ— 10⁹⁢(97-digit number)
80805421064616793898…80986716353511330879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.616 Γ— 10⁹⁷(98-digit number)
16161084212923358779…61973432707022661759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.232 Γ— 10⁹⁷(98-digit number)
32322168425846717559…23946865414045323519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.464 Γ— 10⁹⁷(98-digit number)
64644336851693435118…47893730828090647039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.292 Γ— 10⁹⁸(99-digit number)
12928867370338687023…95787461656181294079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.585 Γ— 10⁹⁸(99-digit number)
25857734740677374047…91574923312362588159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.171 Γ— 10⁹⁸(99-digit number)
51715469481354748094…83149846624725176319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.034 Γ— 10⁹⁹(100-digit number)
10343093896270949618…66299693249450352639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.068 Γ— 10⁹⁹(100-digit number)
20686187792541899237…32599386498900705279
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 103610

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 08eb83c4576ff698584d93d8437327b20b0e54f1ef85ca1ac1432639cbbe509d

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 #103,610 on Chainz β†—
Circulating Supply:57,857,460 XPMΒ·at block #6,826,663 Β· updates every 60s
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