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Block #694,644

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/27/2014, 2:00:04 AM Β· Difficulty 10.9573 Β· 6,116,430 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d9fc9e820f18d5528d79b625e9fd854ad81839623d5f6fead8f8d103b9b6f248
View on Chainz β†—

Height

#694,644

Difficulty

10.957342

Transactions

2

Size

546 B

Version

2

Bits

0af5145c

Nonce

110,603,660

Timestamp

8/27/2014, 2:00:04 AM

Confirmations

6,116,430

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bd674dc75c8d81d7f1b5efadda521c9e18f64aa97038c0b3c3332db325179156
Transactions (2)
Coinbasec41dbe23a5e90d…ac7e02355963b8
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
5fd63261db2b09…8f3d78158c5051
2 in β†’ 1 out1.7360 XPM340 B
AGZdXaTH…1eWCc5d1
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.

1.658 Γ— 10⁹⁡(96-digit number)
16580381262936029431…68499920177591870081
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
1.658 Γ— 10⁹⁡(96-digit number)
16580381262936029431…68499920177591870081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.316 Γ— 10⁹⁡(96-digit number)
33160762525872058863…36999840355183740161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.632 Γ— 10⁹⁡(96-digit number)
66321525051744117726…73999680710367480321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.326 Γ— 10⁹⁢(97-digit number)
13264305010348823545…47999361420734960641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.652 Γ— 10⁹⁢(97-digit number)
26528610020697647090…95998722841469921281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.305 Γ— 10⁹⁢(97-digit number)
53057220041395294181…91997445682939842561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.061 Γ— 10⁹⁷(98-digit number)
10611444008279058836…83994891365879685121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.122 Γ— 10⁹⁷(98-digit number)
21222888016558117672…67989782731759370241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.244 Γ— 10⁹⁷(98-digit number)
42445776033116235344…35979565463518740481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.489 Γ— 10⁹⁷(98-digit number)
84891552066232470689…71959130927037480961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.697 Γ— 10⁹⁸(99-digit number)
16978310413246494137…43918261854074961921
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:57,732,697 XPMΒ·at block #6,811,073 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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