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Block #634,938

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2014, 8:12:49 PM Β· Difficulty 10.9642 Β· 6,164,420 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8bd7e941d363ab5da5351e5876bdfbb32a65aecb3bf0e7509a04fa575ad259d2
View on Chainz β†—

Height

#634,938

Difficulty

10.964238

Transactions

3

Size

2.34 KB

Version

2

Bits

0af6d848

Nonce

1,074,655,877

Timestamp

7/15/2014, 8:12:49 PM

Confirmations

6,164,420

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f8c7247379a290aec2f4ddc00c9ef41fa81ea185dc7dd3a08ba8be74af12c8e0
Transactions (3)
Coinbaseb10d6b4a99b503…fbeed68371e77c
1 in β†’ 1 out8.3500 XPM116 B
ANSXnLY2…Sd25TjkD
08018a864c106b…8398ae8dabf6f6
13 in β†’ 1 out27.0919 XPM1.92 KB
AUfFUyLC…Yn2PxLEq
2e56c1ae701175…22ee1cfad6025d
1 in β†’ 2 out2.0860 XPM225 B
AS9ZCvju…bu3NEFwZAaDrryB7…3mnpVGG3
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.

9.363 Γ— 10⁹⁴(95-digit number)
93639743274230775725…90219398600151294721
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
9.363 Γ— 10⁹⁴(95-digit number)
93639743274230775725…90219398600151294721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.872 Γ— 10⁹⁡(96-digit number)
18727948654846155145…80438797200302589441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.745 Γ— 10⁹⁡(96-digit number)
37455897309692310290…60877594400605178881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.491 Γ— 10⁹⁡(96-digit number)
74911794619384620580…21755188801210357761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.498 Γ— 10⁹⁢(97-digit number)
14982358923876924116…43510377602420715521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.996 Γ— 10⁹⁢(97-digit number)
29964717847753848232…87020755204841431041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.992 Γ— 10⁹⁢(97-digit number)
59929435695507696464…74041510409682862081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.198 Γ— 10⁹⁷(98-digit number)
11985887139101539292…48083020819365724161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.397 Γ— 10⁹⁷(98-digit number)
23971774278203078585…96166041638731448321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.794 Γ— 10⁹⁷(98-digit number)
47943548556406157171…92332083277462896641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.588 Γ— 10⁹⁷(98-digit number)
95887097112812314342…84664166554925793281
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:57,638,910 XPMΒ·at block #6,799,357 Β· updates every 60s
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