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Block #2,056,516

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/5/2017, 9:51:04 AM Β· Difficulty 10.8217 Β· 4,788,425 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
056dd2cad70a6a7ff4adebeac874ce40ce83936b72ac3ec670769966acc0ab00
View on Chainz β†—

Height

#2,056,516

Difficulty

10.821731

Transactions

1

Size

199 B

Version

2

Bits

0ad25cf2

Nonce

532,275,698

Timestamp

4/5/2017, 9:51:04 AM

Confirmations

4,788,425

Mined by

⛏️ P2SHASJZEmAS9NyiiAjRa4mXbsY7oNYJbSPpbf

Merkle Root

b49a6930b9a6ce58ee3ead6317820347c6bd021149b6270b1ed65149ede7f1b4
Transactions (1)
Coinbaseb49a6930b9a6ce…d65149ede7f1b4
1 in β†’ 1 out8.5300 XPM109 B
ASJZEmAS…YJbSPpbf
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.

2.428 Γ— 10⁹⁡(96-digit number)
24287947873638565460…59936244259479770879
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
2.428 Γ— 10⁹⁡(96-digit number)
24287947873638565460…59936244259479770879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.857 Γ— 10⁹⁡(96-digit number)
48575895747277130920…19872488518959541759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.715 Γ— 10⁹⁡(96-digit number)
97151791494554261840…39744977037919083519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.943 Γ— 10⁹⁢(97-digit number)
19430358298910852368…79489954075838167039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.886 Γ— 10⁹⁢(97-digit number)
38860716597821704736…58979908151676334079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.772 Γ— 10⁹⁢(97-digit number)
77721433195643409472…17959816303352668159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.554 Γ— 10⁹⁷(98-digit number)
15544286639128681894…35919632606705336319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.108 Γ— 10⁹⁷(98-digit number)
31088573278257363788…71839265213410672639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.217 Γ— 10⁹⁷(98-digit number)
62177146556514727577…43678530426821345279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.243 Γ— 10⁹⁸(99-digit number)
12435429311302945515…87357060853642690559
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:58,003,947 XPMΒ·at block #6,844,940 Β· updates every 60s
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