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Block #706,514

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/4/2014, 5:28:06 AM Β· Difficulty 10.9589 Β· 6,120,431 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
110d7a1a57b71770a5f60b7e3fa78c07d21984136d8dea015e9391cf2a02ac8b
View on Chainz β†—

Height

#706,514

Difficulty

10.958904

Transactions

2

Size

693 B

Version

2

Bits

0af57ab9

Nonce

796,594,808

Timestamp

9/4/2014, 5:28:06 AM

Confirmations

6,120,431

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8d55eec03133cee69624ef55f5c4e6c1499433ccbbd665abe35753ffe80c1c9e
Transactions (2)
Coinbasef2bc2e55727211…4d0d769963b991
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
014cb5c32c8115…e8986ddd7fcba1
3 in β†’ 1 out98.6100 XPM486 B
AT17cFES…pVkn4hgW
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.

6.663 Γ— 10⁹⁡(96-digit number)
66639789786974372680…15318491199365710801
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
6.663 Γ— 10⁹⁡(96-digit number)
66639789786974372680…15318491199365710801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.332 Γ— 10⁹⁢(97-digit number)
13327957957394874536…30636982398731421601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.665 Γ— 10⁹⁢(97-digit number)
26655915914789749072…61273964797462843201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.331 Γ— 10⁹⁢(97-digit number)
53311831829579498144…22547929594925686401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.066 Γ— 10⁹⁷(98-digit number)
10662366365915899628…45095859189851372801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.132 Γ— 10⁹⁷(98-digit number)
21324732731831799257…90191718379702745601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.264 Γ— 10⁹⁷(98-digit number)
42649465463663598515…80383436759405491201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.529 Γ— 10⁹⁷(98-digit number)
85298930927327197030…60766873518810982401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.705 Γ— 10⁹⁸(99-digit number)
17059786185465439406…21533747037621964801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.411 Γ— 10⁹⁸(99-digit number)
34119572370930878812…43067494075243929601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.823 Γ— 10⁹⁸(99-digit number)
68239144741861757624…86134988150487859201
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:57,859,735 XPMΒ·at block #6,826,944 Β· updates every 60s
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