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Block #2,716,250

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/22/2018, 9:31:43 AM Β· Difficulty 11.6142 Β· 4,122,701 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4398c7b1373bac0094163d1bd76eabcc39df03cfdcc03415d6fc7b4701c7d54b
View on Chainz β†—

Height

#2,716,250

Difficulty

11.614161

Transactions

1

Size

199 B

Version

2

Bits

0b9d39a5

Nonce

134,053,973

Timestamp

6/22/2018, 9:31:43 AM

Confirmations

4,122,701

Mined by

⛏️ P2SHAciWjnrji3mEWtcCuZu41q22CP8d3EqPyL

Merkle Root

e27979f52fe83709761bef96aea6dfc7d694d92dbfd292c697d1c17a291c28a7
Transactions (1)
Coinbasee27979f52fe837…d1c17a291c28a7
1 in β†’ 1 out7.4000 XPM109 B
AciWjnrj…8d3EqPyL
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.

2.967 Γ— 10⁹⁴(95-digit number)
29671122064981216506…18789406270239781119
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
2.967 Γ— 10⁹⁴(95-digit number)
29671122064981216506…18789406270239781119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.934 Γ— 10⁹⁴(95-digit number)
59342244129962433013…37578812540479562239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.186 Γ— 10⁹⁡(96-digit number)
11868448825992486602…75157625080959124479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.373 Γ— 10⁹⁡(96-digit number)
23736897651984973205…50315250161918248959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.747 Γ— 10⁹⁡(96-digit number)
47473795303969946410…00630500323836497919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.494 Γ— 10⁹⁡(96-digit number)
94947590607939892821…01261000647672995839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.898 Γ— 10⁹⁢(97-digit number)
18989518121587978564…02522001295345991679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.797 Γ— 10⁹⁢(97-digit number)
37979036243175957128…05044002590691983359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.595 Γ— 10⁹⁢(97-digit number)
75958072486351914256…10088005181383966719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.519 Γ— 10⁹⁷(98-digit number)
15191614497270382851…20176010362767933439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.038 Γ— 10⁹⁷(98-digit number)
30383228994540765702…40352020725535866879
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:57,955,875 XPMΒ·at block #6,838,950 Β· updates every 60s
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