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Block #2,287,972

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/8/2017, 3:19:17 PM Β· Difficulty 10.9555 Β· 4,555,250 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5278a77afa7ab7c94bbd52f3999dd0f0e7aa4db5a265bc0e141e6f26ea68917e
View on Chainz β†—

Height

#2,287,972

Difficulty

10.955481

Transactions

1

Size

200 B

Version

2

Bits

0af49a63

Nonce

61,749,640

Timestamp

9/8/2017, 3:19:17 PM

Confirmations

4,555,250

Mined by

⛏️ P2SHAU5aWw59Gv5mbHvsQdGNEGb42yUqoM4o5k

Merkle Root

9f33b5d9f67362792a0d07e91c1a389390ead58371bcdea5229bbe090403cf10
Transactions (1)
Coinbase9f33b5d9f67362…9bbe090403cf10
1 in β†’ 1 out8.3200 XPM109 B
AU5aWw59…UqoM4o5k
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.

5.772 Γ— 10⁹⁢(97-digit number)
57722107849415908305…62495095659748915201
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
5.772 Γ— 10⁹⁢(97-digit number)
57722107849415908305…62495095659748915201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.154 Γ— 10⁹⁷(98-digit number)
11544421569883181661…24990191319497830401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.308 Γ— 10⁹⁷(98-digit number)
23088843139766363322…49980382638995660801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.617 Γ— 10⁹⁷(98-digit number)
46177686279532726644…99960765277991321601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.235 Γ— 10⁹⁷(98-digit number)
92355372559065453289…99921530555982643201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.847 Γ— 10⁹⁸(99-digit number)
18471074511813090657…99843061111965286401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.694 Γ— 10⁹⁸(99-digit number)
36942149023626181315…99686122223930572801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.388 Γ— 10⁹⁸(99-digit number)
73884298047252362631…99372244447861145601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.477 Γ— 10⁹⁹(100-digit number)
14776859609450472526…98744488895722291201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.955 Γ— 10⁹⁹(100-digit number)
29553719218900945052…97488977791444582401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.910 Γ— 10⁹⁹(100-digit number)
59107438437801890105…94977955582889164801
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:57,990,150 XPMΒ·at block #6,843,221 Β· updates every 60s
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