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Block #4,000,310

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/20/2020, 4:11:17 PM Β· Difficulty 10.8400 Β· 2,817,567 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9c1ee2adc37d4f9d2269bb84fb475db9207dcd79d2fd7d427a24b2b786596dfe
View on Chainz β†—

Height

#4,000,310

Difficulty

10.839975

Transactions

1

Size

200 B

Version

2

Bits

0ad7089d

Nonce

287,965,785

Timestamp

12/20/2020, 4:11:17 PM

Confirmations

2,817,567

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

e1ef586376b7d01bbe11d5bc31dd790f1335f52f2325c4df5dd38ba963a58e77
Transactions (1)
Coinbasee1ef586376b7d0…d38ba963a58e77
1 in β†’ 1 out8.5000 XPM109 B
ASiq2qtK…VMhmk7yL
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.

6.905 Γ— 10⁹⁢(97-digit number)
69054264958555819382…72710690007080304639
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
6.905 Γ— 10⁹⁢(97-digit number)
69054264958555819382…72710690007080304639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.381 Γ— 10⁹⁷(98-digit number)
13810852991711163876…45421380014160609279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.762 Γ— 10⁹⁷(98-digit number)
27621705983422327753…90842760028321218559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.524 Γ— 10⁹⁷(98-digit number)
55243411966844655506…81685520056642437119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.104 Γ— 10⁹⁸(99-digit number)
11048682393368931101…63371040113284874239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.209 Γ— 10⁹⁸(99-digit number)
22097364786737862202…26742080226569748479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.419 Γ— 10⁹⁸(99-digit number)
44194729573475724405…53484160453139496959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.838 Γ— 10⁹⁸(99-digit number)
88389459146951448810…06968320906278993919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.767 Γ— 10⁹⁹(100-digit number)
17677891829390289762…13936641812557987839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.535 Γ— 10⁹⁹(100-digit number)
35355783658780579524…27873283625115975679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,787,075 XPMΒ·at block #6,817,876 Β· updates every 60s
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