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Block #11,946

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/11/2013, 8:14:46 AM Β· Difficulty 7.7410 Β· 6,795,513 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b41c40c9fe1f915bcaa5afc5d285f2eab3005d866c7532e35dfcfd5733620856
View on Chainz β†—

Height

#11,946

Difficulty

7.741020

Transactions

1

Size

196 B

Version

2

Bits

07bdb380

Nonce

32

Timestamp

7/11/2013, 8:14:46 AM

Confirmations

6,795,513

Mined by

⛏️ P2SHAdWHv8yonFfCMPM3Ss72GYKPuZ8LoH1JaP

Merkle Root

0decb4c1fdbb8ff2c93cee6a7e959433ffaaf83e889811c28cfa7db6ebd513c2
Transactions (1)
Coinbase0decb4c1fdbb8f…fa7db6ebd513c2
1 in β†’ 1 out16.6700 XPM108 B
AdWHv8yo…8LoH1JaP
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.

8.172 Γ— 10⁸⁸(89-digit number)
81728493437874865335…18323031598579726739
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
8.172 Γ— 10⁸⁸(89-digit number)
81728493437874865335…18323031598579726739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.634 Γ— 10⁸⁹(90-digit number)
16345698687574973067…36646063197159453479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.269 Γ— 10⁸⁹(90-digit number)
32691397375149946134…73292126394318906959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.538 Γ— 10⁸⁹(90-digit number)
65382794750299892268…46584252788637813919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.307 Γ— 10⁹⁰(91-digit number)
13076558950059978453…93168505577275627839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.615 Γ— 10⁹⁰(91-digit number)
26153117900119956907…86337011154551255679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.230 Γ— 10⁹⁰(91-digit number)
52306235800239913814…72674022309102511359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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, …
Cross-reference on Chainz Explorer
Circulating Supply:57,703,696 XPMΒ·at block #6,807,458 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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