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Home/Chain Registry/Block #103,207

Block #103,207

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2013, 11:50:04 AM Β· Difficulty 9.5188 Β· 6,713,056 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ab7ff1ab89f9149c3fa316639334e5b81d5666a90f3d458039892976242dd607
View on Chainz β†—

Height

#103,207

Difficulty

9.518792

Transactions

1

Size

199 B

Version

2

Bits

0984cf94

Nonce

62,003

Timestamp

8/7/2013, 11:50:04 AM

Confirmations

6,713,056

Merkle Root

11b3f21ec89160b8fc253efb8db96b37022eeaa41c5fb5dc9621f416e98a76a7
Transactions (1)
Coinbase11b3f21ec89160…21f416e98a76a7
1 in β†’ 1 out11.0200 XPM109 B
AcM2gGug…87xGTED8
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.

8.542 Γ— 10⁹⁴(95-digit number)
85424516488048998634…92583123565295520000
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
8.542 Γ— 10⁹⁴(95-digit number)
85424516488048998634…92583123565295519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.708 Γ— 10⁹⁡(96-digit number)
17084903297609799726…85166247130591039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.416 Γ— 10⁹⁡(96-digit number)
34169806595219599453…70332494261182079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.833 Γ— 10⁹⁡(96-digit number)
68339613190439198907…40664988522364159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.366 Γ— 10⁹⁢(97-digit number)
13667922638087839781…81329977044728319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.733 Γ— 10⁹⁢(97-digit number)
27335845276175679563…62659954089456639999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.467 Γ— 10⁹⁢(97-digit number)
54671690552351359126…25319908178913279999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.093 Γ— 10⁹⁷(98-digit number)
10934338110470271825…50639816357826559999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.186 Γ— 10⁹⁷(98-digit number)
21868676220940543650…01279632715653119999
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 103207

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 ab7ff1ab89f9149c3fa316639334e5b81d5666a90f3d458039892976242dd607

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 #103,207 on Chainz β†—
Circulating Supply:57,774,217 XPMΒ·at block #6,816,262 Β· updates every 60s
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