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Block #120,933

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/17/2013, 12:00:07 PM Β· Difficulty 9.7517 Β· 6,710,344 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1a0988f66a0484034db5a3cb97db0bc660c758dd72648e2935a6fbfdadf8ec26
View on Chainz β†—

Height

#120,933

Difficulty

9.751653

Transactions

1

Size

199 B

Version

2

Bits

09c06c52

Nonce

96,076

Timestamp

8/17/2013, 12:00:07 PM

Confirmations

6,710,344

Mined by

⛏️ P2SHAU7tifqruS2RhRAdT48vdcfAUbfKVeVw3f

Merkle Root

3e45fedacfc2c532a32fc72fcdb97a5ba625b83b98643a902cc9b3b8c0513344
Transactions (1)
Coinbase3e45fedacfc2c5…c9b3b8c0513344
1 in β†’ 1 out10.5000 XPM109 B
AU7tifqr…fKVeVw3f
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.

9.701 Γ— 10⁹⁴(95-digit number)
97015728039436146526…14756155369454725909
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
9.701 Γ— 10⁹⁴(95-digit number)
97015728039436146526…14756155369454725909
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.940 Γ— 10⁹⁡(96-digit number)
19403145607887229305…29512310738909451819
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.880 Γ— 10⁹⁡(96-digit number)
38806291215774458610…59024621477818903639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.761 Γ— 10⁹⁡(96-digit number)
77612582431548917221…18049242955637807279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.552 Γ— 10⁹⁢(97-digit number)
15522516486309783444…36098485911275614559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.104 Γ— 10⁹⁢(97-digit number)
31045032972619566888…72196971822551229119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.209 Γ— 10⁹⁢(97-digit number)
62090065945239133777…44393943645102458239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.241 Γ— 10⁹⁷(98-digit number)
12418013189047826755…88787887290204916479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.483 Γ— 10⁹⁷(98-digit number)
24836026378095653510…77575774580409832959
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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

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:57,894,359 XPMΒ·at block #6,831,276 Β· updates every 60s
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