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Block #2,747,407

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2018, 4:52:41 PM Β· Difficulty 11.6500 Β· 4,094,819 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dc845bba5955c992198cf58d6ee71f1e46803593fd710449369bd8c772ef1404
View on Chainz β†—

Height

#2,747,407

Difficulty

11.649961

Transactions

1

Size

201 B

Version

2

Bits

0ba663d9

Nonce

586,895,880

Timestamp

7/13/2018, 4:52:41 PM

Confirmations

4,094,819

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

40d5fc2fdae6eeb3bc5e39405d2764628055df8f9862ddc4c703c73ee5e5a479
Transactions (1)
Coinbase40d5fc2fdae6ee…03c73ee5e5a479
1 in β†’ 1 out7.3600 XPM110 B
AZtxQr2F…7grUWrUz
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.

2.344 Γ— 10⁹⁢(97-digit number)
23447287574456922053…59009910662492364799
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
2.344 Γ— 10⁹⁢(97-digit number)
23447287574456922053…59009910662492364799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.689 Γ— 10⁹⁢(97-digit number)
46894575148913844106…18019821324984729599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.378 Γ— 10⁹⁢(97-digit number)
93789150297827688212…36039642649969459199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.875 Γ— 10⁹⁷(98-digit number)
18757830059565537642…72079285299938918399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.751 Γ— 10⁹⁷(98-digit number)
37515660119131075284…44158570599877836799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.503 Γ— 10⁹⁷(98-digit number)
75031320238262150569…88317141199755673599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.500 Γ— 10⁹⁸(99-digit number)
15006264047652430113…76634282399511347199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.001 Γ— 10⁹⁸(99-digit number)
30012528095304860227…53268564799022694399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.002 Γ— 10⁹⁸(99-digit number)
60025056190609720455…06537129598045388799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.200 Γ— 10⁹⁹(100-digit number)
12005011238121944091…13074259196090777599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.401 Γ— 10⁹⁹(100-digit number)
24010022476243888182…26148518392181555199
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:57,982,206 XPMΒ·at block #6,842,225 Β· updates every 60s
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