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Block #3,494,168

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/30/2019, 3:29:14 PM Β· Difficulty 10.9498 Β· 3,311,545 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
effc6c3e2803d79b1287c4d370853312b71f5a989617e998a60aca642ec5a075
View on Chainz β†—

Height

#3,494,168

Difficulty

10.949843

Transactions

2

Size

539 B

Version

2

Bits

0af328e1

Nonce

282,019,433

Timestamp

12/30/2019, 3:29:14 PM

Confirmations

3,311,545

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

c0bc784d939fe0a0bdd1d40df9227625189eb99d97790cffc841b720a4a35383
Transactions (2)
Coinbasefbe0de8221edc4…401bd919ac7d77
1 in β†’ 1 out8.3400 XPM110 B
ASiq2qtK…VMhmk7yL
c3045b4a8bd6cc…b4a612d7a05abe
2 in β†’ 2 out11.6500 XPM340 B
ARpQfN8q…fx8P5LwjALh3G4wq…cFPms2mF
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.

3.735 Γ— 10⁹²(93-digit number)
37356845228361424934…83806455328224708799
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
3.735 Γ— 10⁹²(93-digit number)
37356845228361424934…83806455328224708799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.471 Γ— 10⁹²(93-digit number)
74713690456722849868…67612910656449417599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.494 Γ— 10⁹³(94-digit number)
14942738091344569973…35225821312898835199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.988 Γ— 10⁹³(94-digit number)
29885476182689139947…70451642625797670399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.977 Γ— 10⁹³(94-digit number)
59770952365378279894…40903285251595340799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.195 Γ— 10⁹⁴(95-digit number)
11954190473075655978…81806570503190681599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.390 Γ— 10⁹⁴(95-digit number)
23908380946151311957…63613141006381363199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.781 Γ— 10⁹⁴(95-digit number)
47816761892302623915…27226282012762726399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.563 Γ— 10⁹⁴(95-digit number)
95633523784605247831…54452564025525452799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.912 Γ— 10⁹⁡(96-digit number)
19126704756921049566…08905128051050905599
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:57,689,787 XPMΒ·at block #6,805,712 Β· updates every 60s
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