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Block #2,479,055

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/18/2018, 4:35:14 PM Β· Difficulty 10.9658 Β· 4,360,618 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
eaf7c3e27d76a04886fc230739b9bb04cc60c853610e067fa01053163a14509d
View on Chainz β†—

Height

#2,479,055

Difficulty

10.965805

Transactions

2

Size

867 B

Version

2

Bits

0af73eff

Nonce

147,650,710

Timestamp

1/18/2018, 4:35:14 PM

Confirmations

4,360,618

Mined by

⛏️ P2SHAXPMAgM7qbuRDQP4FnxS4vskNqyKNvEUC7

Merkle Root

909ee33c68561e97a0411f6b2ebe4e7ad79a424ad155ceea563289ee18497b34
Transactions (2)
Coinbase9db409956f6da8…d539aa2d795f84
1 in β†’ 1 out8.3100 XPM109 B
AXPMAgM7…yKNvEUC7
049c56245b7bf6…b6cc7b65fc3a7b
4 in β†’ 2 out2.1714 XPM668 B
APBM2w7U…Qx6F7p89AQZfNwW6…zEpfzFum
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.

1.281 Γ— 10⁹⁴(95-digit number)
12817897005301632247…92364351729419947599
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
1.281 Γ— 10⁹⁴(95-digit number)
12817897005301632247…92364351729419947599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.563 Γ— 10⁹⁴(95-digit number)
25635794010603264495…84728703458839895199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.127 Γ— 10⁹⁴(95-digit number)
51271588021206528991…69457406917679790399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.025 Γ— 10⁹⁡(96-digit number)
10254317604241305798…38914813835359580799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.050 Γ— 10⁹⁡(96-digit number)
20508635208482611596…77829627670719161599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.101 Γ— 10⁹⁡(96-digit number)
41017270416965223193…55659255341438323199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.203 Γ— 10⁹⁡(96-digit number)
82034540833930446387…11318510682876646399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.640 Γ— 10⁹⁢(97-digit number)
16406908166786089277…22637021365753292799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.281 Γ— 10⁹⁢(97-digit number)
32813816333572178554…45274042731506585599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.562 Γ— 10⁹⁢(97-digit number)
65627632667144357109…90548085463013171199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.312 Γ— 10⁹⁷(98-digit number)
13125526533428871421…81096170926026342399
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:57,961,673 XPMΒ·at block #6,839,672 Β· updates every 60s
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