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Block #2,652,521

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/7/2018, 4:29:27 PM Β· Difficulty 11.7437 Β· 4,151,079 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
91d188356ac7a904ef6f96a4bc464a76388afa14d825fff15268af1704fe4506
View on Chainz β†—

Height

#2,652,521

Difficulty

11.743694

Transactions

2

Size

30.62 KB

Version

2

Bits

0bbe62b7

Nonce

622,852,555

Timestamp

5/7/2018, 4:29:27 PM

Confirmations

4,151,079

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

61bb6fbb20fbf85ce7f9ca2136ad8bed624cda9d6715fc79838ee14480b40943
Transactions (2)
Coinbase0e0a5dba40f708…b1a67d259d4e77
1 in β†’ 1 out7.5600 XPM110 B
Adqah8zh…1WwoHJ9t
6ce54437cddb11…91307a1cc6d209
254 in β†’ 1 out1999.7641 XPM30.43 KB
AJo7wBH9…auz44BMp
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.

4.009 Γ— 10⁹⁢(97-digit number)
40098190732885718948…47637929327003847679
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
4.009 Γ— 10⁹⁢(97-digit number)
40098190732885718948…47637929327003847679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.019 Γ— 10⁹⁢(97-digit number)
80196381465771437897…95275858654007695359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.603 Γ— 10⁹⁷(98-digit number)
16039276293154287579…90551717308015390719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.207 Γ— 10⁹⁷(98-digit number)
32078552586308575159…81103434616030781439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.415 Γ— 10⁹⁷(98-digit number)
64157105172617150318…62206869232061562879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.283 Γ— 10⁹⁸(99-digit number)
12831421034523430063…24413738464123125759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.566 Γ— 10⁹⁸(99-digit number)
25662842069046860127…48827476928246251519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.132 Γ— 10⁹⁸(99-digit number)
51325684138093720254…97654953856492503039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.026 Γ— 10⁹⁹(100-digit number)
10265136827618744050…95309907712985006079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.053 Γ— 10⁹⁹(100-digit number)
20530273655237488101…90619815425970012159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.106 Γ— 10⁹⁹(100-digit number)
41060547310474976203…81239630851940024319
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:57,672,838 XPMΒ·at block #6,803,599 Β· updates every 60s
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