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Block #2,998,673

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/7/2019, 12:08:20 AM Β· Difficulty 11.2363 Β· 3,835,116 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f851bac6c2f07e3715504b4cc2a5309cf8e4dec1a3b28815981fa61ba56de854
View on Chainz β†—

Height

#2,998,673

Difficulty

11.236280

Transactions

2

Size

1017 B

Version

2

Bits

0b3c7cd4

Nonce

1,618,632,788

Timestamp

1/7/2019, 12:08:20 AM

Confirmations

3,835,116

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

5b340b491077ff787c15f1a46a560199e37e85a0ce410a7c2637a574385216ed
Transactions (2)
Coinbase9c4b6fd5e360f2…a7b97d20bae464
1 in β†’ 1 out7.9200 XPM110 B
AbXwmGxD…4XXYP765
e4bf00e4868ddf…b31f555b297520
5 in β†’ 2 out158.9943 XPM817 B
AbadyHGq…syxq2CpkAGEfgVr4…489751Bm
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.

7.567 Γ— 10⁹⁴(95-digit number)
75674078870703686376…12241943600203295201
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
7.567 Γ— 10⁹⁴(95-digit number)
75674078870703686376…12241943600203295201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.513 Γ— 10⁹⁡(96-digit number)
15134815774140737275…24483887200406590401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.026 Γ— 10⁹⁡(96-digit number)
30269631548281474550…48967774400813180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.053 Γ— 10⁹⁡(96-digit number)
60539263096562949101…97935548801626361601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.210 Γ— 10⁹⁢(97-digit number)
12107852619312589820…95871097603252723201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.421 Γ— 10⁹⁢(97-digit number)
24215705238625179640…91742195206505446401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.843 Γ— 10⁹⁢(97-digit number)
48431410477250359280…83484390413010892801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.686 Γ— 10⁹⁢(97-digit number)
96862820954500718561…66968780826021785601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.937 Γ— 10⁹⁷(98-digit number)
19372564190900143712…33937561652043571201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.874 Γ— 10⁹⁷(98-digit number)
38745128381800287424…67875123304087142401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.749 Γ— 10⁹⁷(98-digit number)
77490256763600574849…35750246608174284801
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,914,532 XPMΒ·at block #6,833,788 Β· updates every 60s
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