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Block #2,797,060

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2018, 9:43:45 PM Β· Difficulty 11.6787 Β· 4,045,729 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5f019e8af4fe69a38eec2748a06556c3eab0cf6957da38aca7a9b5d585ab3afa
View on Chainz β†—

Height

#2,797,060

Difficulty

11.678733

Transactions

2

Size

426 B

Version

2

Bits

0badc174

Nonce

1,359,563,148

Timestamp

8/16/2018, 9:43:45 PM

Confirmations

4,045,729

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

a09307f3568a94c83b00ee20a7d32437b251fad0deea048305e5c10dbf225c70
Transactions (2)
Coinbase56ab13b87b80d7…7427c36885cff9
1 in β†’ 1 out7.3300 XPM109 B
AZtxQr2F…7grUWrUz
9f2173f6a02b7c…03232bae21f715
1 in β†’ 2 out3.9900 XPM227 B
AUepM3vs…SYxWnP2AARkhA3cy…WE7nESAq
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.

5.177 Γ— 10⁹³(94-digit number)
51774850986100081270…21911476901497516549
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
5.177 Γ— 10⁹³(94-digit number)
51774850986100081270…21911476901497516549
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.035 Γ— 10⁹⁴(95-digit number)
10354970197220016254…43822953802995033099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.070 Γ— 10⁹⁴(95-digit number)
20709940394440032508…87645907605990066199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.141 Γ— 10⁹⁴(95-digit number)
41419880788880065016…75291815211980132399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.283 Γ— 10⁹⁴(95-digit number)
82839761577760130032…50583630423960264799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.656 Γ— 10⁹⁡(96-digit number)
16567952315552026006…01167260847920529599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.313 Γ— 10⁹⁡(96-digit number)
33135904631104052013…02334521695841059199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.627 Γ— 10⁹⁡(96-digit number)
66271809262208104026…04669043391682118399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.325 Γ— 10⁹⁢(97-digit number)
13254361852441620805…09338086783364236799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.650 Γ— 10⁹⁢(97-digit number)
26508723704883241610…18676173566728473599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.301 Γ— 10⁹⁢(97-digit number)
53017447409766483221…37352347133456947199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,986,650 XPMΒ·at block #6,842,788 Β· updates every 60s
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