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Block #2,047,647

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/1/2017, 4:52:00 AM Β· Difficulty 10.6870 Β· 4,792,835 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3269dfb5ea3fc74758e28297720d00609d481544e2cfd4d9762196f7badda9bf
View on Chainz β†—

Height

#2,047,647

Difficulty

10.686981

Transactions

1

Size

200 B

Version

2

Bits

0aafddf9

Nonce

817,718,557

Timestamp

4/1/2017, 4:52:00 AM

Confirmations

4,792,835

Mined by

⛏️ P2SHAZqu1Tm5gAhLzH5buJF9GZYo3Uy7hWPvYy

Merkle Root

df1adc0d743e7c7f287724c2a9df47c6e4596728b3490a74e013ca7e0860950f
Transactions (1)
Coinbasedf1adc0d743e7c…13ca7e0860950f
1 in β†’ 1 out8.7400 XPM110 B
AZqu1Tm5…y7hWPvYy
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.

3.755 Γ— 10⁹⁴(95-digit number)
37557979586820333292…96056137602138951681
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
3.755 Γ— 10⁹⁴(95-digit number)
37557979586820333292…96056137602138951681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.511 Γ— 10⁹⁴(95-digit number)
75115959173640666584…92112275204277903361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.502 Γ— 10⁹⁡(96-digit number)
15023191834728133316…84224550408555806721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.004 Γ— 10⁹⁡(96-digit number)
30046383669456266633…68449100817111613441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.009 Γ— 10⁹⁡(96-digit number)
60092767338912533267…36898201634223226881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.201 Γ— 10⁹⁢(97-digit number)
12018553467782506653…73796403268446453761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.403 Γ— 10⁹⁢(97-digit number)
24037106935565013307…47592806536892907521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.807 Γ— 10⁹⁢(97-digit number)
48074213871130026614…95185613073785815041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.614 Γ— 10⁹⁢(97-digit number)
96148427742260053228…90371226147571630081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.922 Γ— 10⁹⁷(98-digit number)
19229685548452010645…80742452295143260161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.845 Γ— 10⁹⁷(98-digit number)
38459371096904021291…61484904590286520321
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:57,968,186 XPMΒ·at block #6,840,481 Β· updates every 60s
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