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Block #2,833,148

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 1:28:21 PM Β· Difficulty 11.7149 Β· 4,009,237 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bbcd48afa789b74e0bbe1d0daf8ad3b78f924b06ab9228a398efd12ede145284
View on Chainz β†—

Height

#2,833,148

Difficulty

11.714852

Transactions

1

Size

200 B

Version

2

Bits

0bb7008d

Nonce

314,022,520

Timestamp

9/10/2018, 1:28:21 PM

Confirmations

4,009,237

Mined by

⛏️ P2SHATbynJEZ1Hx72sWSRrMfVoUUHa1PxFUyTe

Merkle Root

259a65e4b2de6ace4cd57ba375784e608ff7bc13243a701c407806659aa92450
Transactions (1)
Coinbase259a65e4b2de6a…7806659aa92450
1 in β†’ 1 out7.2700 XPM110 B
ATbynJEZ…1PxFUyTe
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.

2.900 Γ— 10⁹⁴(95-digit number)
29000051272108426093…74753815112444419879
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
2.900 Γ— 10⁹⁴(95-digit number)
29000051272108426093…74753815112444419879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.800 Γ— 10⁹⁴(95-digit number)
58000102544216852186…49507630224888839759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.160 Γ— 10⁹⁡(96-digit number)
11600020508843370437…99015260449777679519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.320 Γ— 10⁹⁡(96-digit number)
23200041017686740874…98030520899555359039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.640 Γ— 10⁹⁡(96-digit number)
46400082035373481748…96061041799110718079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.280 Γ— 10⁹⁡(96-digit number)
92800164070746963497…92122083598221436159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.856 Γ— 10⁹⁢(97-digit number)
18560032814149392699…84244167196442872319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.712 Γ— 10⁹⁢(97-digit number)
37120065628298785399…68488334392885744639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.424 Γ— 10⁹⁢(97-digit number)
74240131256597570798…36976668785771489279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.484 Γ— 10⁹⁷(98-digit number)
14848026251319514159…73953337571542978559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.969 Γ— 10⁹⁷(98-digit number)
29696052502639028319…47906675143085957119
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:57,983,489 XPMΒ·at block #6,842,384 Β· updates every 60s
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