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Block #164,757

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/14/2013, 8:53:51 PM Β· Difficulty 9.8637 Β· 6,631,186 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
785724b559d5af4435e5b5e2a8c44a83bb27b197b4018aeb6f9c7863d26d0070
View on Chainz β†—

Height

#164,757

Difficulty

9.863736

Transactions

1

Size

198 B

Version

2

Bits

09dd1dc6

Nonce

42,194

Timestamp

9/14/2013, 8:53:51 PM

Confirmations

6,631,186

Mined by

⛏️ P2SHAYc3QGYaSv1sA3FuuZuBoiE4ttSWDuszQp

Merkle Root

af126dd4703213cd7bc7c0940258c22c9a9f7ce065c0e8939edef1fb058d94bd
Transactions (1)
Coinbaseaf126dd4703213…def1fb058d94bd
1 in β†’ 1 out10.2600 XPM109 B
AYc3QGYa…SWDuszQp
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.

1.890 Γ— 10⁹³(94-digit number)
18907928837752907592…02148350367988581761
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
1.890 Γ— 10⁹³(94-digit number)
18907928837752907592…02148350367988581761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.781 Γ— 10⁹³(94-digit number)
37815857675505815185…04296700735977163521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.563 Γ— 10⁹³(94-digit number)
75631715351011630370…08593401471954327041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.512 Γ— 10⁹⁴(95-digit number)
15126343070202326074…17186802943908654081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.025 Γ— 10⁹⁴(95-digit number)
30252686140404652148…34373605887817308161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.050 Γ— 10⁹⁴(95-digit number)
60505372280809304296…68747211775634616321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.210 Γ— 10⁹⁡(96-digit number)
12101074456161860859…37494423551269232641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.420 Γ— 10⁹⁡(96-digit number)
24202148912323721718…74988847102538465281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.840 Γ— 10⁹⁡(96-digit number)
48404297824647443437…49977694205076930561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,611,632 XPMΒ·at block #6,795,942 Β· updates every 60s
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