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Block #2,272,612

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/29/2017, 12:36:37 AM Β· Difficulty 10.9543 Β· 4,571,827 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6c29d18927227eead60078da9983223445aa7a3fbdf195b14f6a1f0944a53c64
View on Chainz β†—

Height

#2,272,612

Difficulty

10.954342

Transactions

2

Size

870 B

Version

2

Bits

0af44fc3

Nonce

1,980,091,866

Timestamp

8/29/2017, 12:36:37 AM

Confirmations

4,571,827

Mined by

⛏️ P2SHAGgHWUzURq4AJNu98iXvS7pEQF1SpwYutP

Merkle Root

77b6df55da10226aae145ee51653a6adc5f04e5236835b8ec2d1bcb4e9136ab2
Transactions (2)
Coinbase1cb2ee83d67d0d…dd53906b7b3a0a
1 in β†’ 1 out8.3300 XPM110 B
AGgHWUzU…1SpwYutP
f016c388ade694…5238348adc4298
4 in β†’ 2 out880.3162 XPM670 B
APpd26Px…tTaorvF5ALgxzFP7…JkXTt8HL
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.

1.211 Γ— 10⁹⁡(96-digit number)
12115677661342321724…46438815518062861121
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
1.211 Γ— 10⁹⁡(96-digit number)
12115677661342321724…46438815518062861121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.423 Γ— 10⁹⁡(96-digit number)
24231355322684643448…92877631036125722241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.846 Γ— 10⁹⁡(96-digit number)
48462710645369286897…85755262072251444481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.692 Γ— 10⁹⁡(96-digit number)
96925421290738573795…71510524144502888961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.938 Γ— 10⁹⁢(97-digit number)
19385084258147714759…43021048289005777921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.877 Γ— 10⁹⁢(97-digit number)
38770168516295429518…86042096578011555841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.754 Γ— 10⁹⁢(97-digit number)
77540337032590859036…72084193156023111681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.550 Γ— 10⁹⁷(98-digit number)
15508067406518171807…44168386312046223361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.101 Γ— 10⁹⁷(98-digit number)
31016134813036343614…88336772624092446721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.203 Γ— 10⁹⁷(98-digit number)
62032269626072687229…76673545248184893441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.240 Γ— 10⁹⁸(99-digit number)
12406453925214537445…53347090496369786881
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:57,999,908 XPMΒ·at block #6,844,438 Β· updates every 60s
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