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Block #2,212,237

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2017, 4:15:04 PM Β· Difficulty 10.9442 Β· 4,630,006 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
108b8c14c95f2ed6c016a2ef1baf6b649ff0ccb4b38987b79f25756790ae4a78
View on Chainz β†—

Height

#2,212,237

Difficulty

10.944157

Transactions

3

Size

653 B

Version

2

Bits

0af1b446

Nonce

134,956,647

Timestamp

7/18/2017, 4:15:04 PM

Confirmations

4,630,006

Mined by

⛏️ P2SHAPmiwH5MsRGoMHNdHX43nyqcMuQ1BL476s

Merkle Root

3e36f71c66dc12ac0e13fd61c289ae0ec833d737b7525172c9613d1e4ca89882
Transactions (3)
Coinbase1f15b523f2a660…9a8d960826a5a8
1 in β†’ 1 out8.3600 XPM110 B
APmiwH5M…Q1BL476s
64a30bc42ce02e…0c9b7e8f36a323
1 in β†’ 2 out182004.6277 XPM227 B
ASKyPKZJ…762eNp3pAMpi61KT…1EVd8d5S
ad5cc8fb65d22d…70ef685ec22205
1 in β†’ 2 out64191.6471 XPM226 B
AM8M6Q97…4831ACoXAMNqyy2W…ise9w8w1
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.

1.961 Γ— 10⁹⁡(96-digit number)
19611141797606631181…39744469138613937921
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
1.961 Γ— 10⁹⁡(96-digit number)
19611141797606631181…39744469138613937921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.922 Γ— 10⁹⁡(96-digit number)
39222283595213262362…79488938277227875841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.844 Γ— 10⁹⁡(96-digit number)
78444567190426524724…58977876554455751681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.568 Γ— 10⁹⁢(97-digit number)
15688913438085304944…17955753108911503361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.137 Γ— 10⁹⁢(97-digit number)
31377826876170609889…35911506217823006721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.275 Γ— 10⁹⁢(97-digit number)
62755653752341219779…71823012435646013441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.255 Γ— 10⁹⁷(98-digit number)
12551130750468243955…43646024871292026881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.510 Γ— 10⁹⁷(98-digit number)
25102261500936487911…87292049742584053761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.020 Γ— 10⁹⁷(98-digit number)
50204523001872975823…74584099485168107521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.004 Γ— 10⁹⁸(99-digit number)
10040904600374595164…49168198970336215041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,982,342 XPMΒ·at block #6,842,242 Β· updates every 60s
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