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Block #2,925,095

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/16/2018, 7:16:54 AM Β· Difficulty 11.3549 Β· 3,911,981 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
24a754d2112b86fa491e1971219a712d5b362b771e02912fe12225d6261b9a70
View on Chainz β†—

Height

#2,925,095

Difficulty

11.354927

Transactions

11

Size

72.90 KB

Version

2

Bits

0b5adc78

Nonce

38,852,506

Timestamp

11/16/2018, 7:16:54 AM

Confirmations

3,911,981

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

fcd64655e6feaa6ec2c68d57ab451daaf000b9ff0b5f4e40859d72ca7fd58124
Transactions (11)
Coinbase02353ad57dca8d…26d16d74b7e77c
1 in β†’ 1 out8.5400 XPM110 B
AUMQRepm…tAfKmdW1
5f39b0f5827f4b…4fc3d5604e5a38
50 in β†’ 1 out234.0291 XPM7.27 KB
AUa77BY6…9ADYWrhb
e400b08544ae9a…eee73a29c2f410
50 in β†’ 1 out255.1483 XPM7.27 KB
AUa77BY6…9ADYWrhb
27536f0d2c3992…67db24bd15f3e5
50 in β†’ 1 out263.8727 XPM7.27 KB
AUa77BY6…9ADYWrhb
7d09cc581c59c8…89bb979dce7321
50 in β†’ 1 out231.3262 XPM7.27 KB
AUa77BY6…9ADYWrhb
90129635803d40…0a38b1aa6327fd
50 in β†’ 1 out217.3603 XPM7.26 KB
AUa77BY6…9ADYWrhb
d8a1e984d6782d…eab3812ed49af6
50 in β†’ 1 out223.2401 XPM7.27 KB
AUa77BY6…9ADYWrhb
d13fe58f940d92…a43f7affd680e7
50 in β†’ 1 out248.3486 XPM7.27 KB
AUa77BY6…9ADYWrhb
03c00e04e4012e…70f3283d158251
50 in β†’ 1 out211.3524 XPM7.27 KB
AUa77BY6…9ADYWrhb
2f4ebd16c3d31f…a1af3de8a22c7c
50 in β†’ 1 out218.9281 XPM7.27 KB
AUa77BY6…9ADYWrhb
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.

1.224 Γ— 10⁹⁷(98-digit number)
12242301578047157401…32107002421262146559
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
1.224 Γ— 10⁹⁷(98-digit number)
12242301578047157401…32107002421262146559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.448 Γ— 10⁹⁷(98-digit number)
24484603156094314803…64214004842524293119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.896 Γ— 10⁹⁷(98-digit number)
48969206312188629606…28428009685048586239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.793 Γ— 10⁹⁷(98-digit number)
97938412624377259213…56856019370097172479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.958 Γ— 10⁹⁸(99-digit number)
19587682524875451842…13712038740194344959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.917 Γ— 10⁹⁸(99-digit number)
39175365049750903685…27424077480388689919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.835 Γ— 10⁹⁸(99-digit number)
78350730099501807370…54848154960777379839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.567 Γ— 10⁹⁹(100-digit number)
15670146019900361474…09696309921554759679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.134 Γ— 10⁹⁹(100-digit number)
31340292039800722948…19392619843109519359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.268 Γ— 10⁹⁹(100-digit number)
62680584079601445896…38785239686219038719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.253 Γ— 10¹⁰⁰(101-digit number)
12536116815920289179…77570479372438077439
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:57,940,910 XPMΒ·at block #6,837,075 Β· updates every 60s
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