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Block #705,505

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/3/2014, 12:05:00 PM Β· Difficulty 10.9591 Β· 6,104,060 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f747bd8bf495d28dacbd6e1a103565b2a64ace88a3f827f6581af5003d20b572
View on Chainz β†—

Height

#705,505

Difficulty

10.959138

Transactions

2

Size

728 B

Version

2

Bits

0af58a17

Nonce

15,651,977

Timestamp

9/3/2014, 12:05:00 PM

Confirmations

6,104,060

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8365845d6d08893cc29d27ff9dc567a53c781af06b543eec4ba455f21cf958d2
Transactions (2)
Coinbase8f3e6b10c10f2b…3bba4eb4ba16ee
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
27c7a4ab2f0f44…52453f602a624a
3 in β†’ 2 out2.3883 XPM521 B
AKinBSz6…c5jHh6RZAeKNrjNj…1NEq95Ta
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.

6.959 Γ— 10⁹⁢(97-digit number)
69597077144915460529…70157469392781134081
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
6.959 Γ— 10⁹⁢(97-digit number)
69597077144915460529…70157469392781134081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.391 Γ— 10⁹⁷(98-digit number)
13919415428983092105…40314938785562268161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.783 Γ— 10⁹⁷(98-digit number)
27838830857966184211…80629877571124536321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.567 Γ— 10⁹⁷(98-digit number)
55677661715932368423…61259755142249072641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.113 Γ— 10⁹⁸(99-digit number)
11135532343186473684…22519510284498145281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.227 Γ— 10⁹⁸(99-digit number)
22271064686372947369…45039020568996290561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.454 Γ— 10⁹⁸(99-digit number)
44542129372745894739…90078041137992581121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.908 Γ— 10⁹⁸(99-digit number)
89084258745491789478…80156082275985162241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.781 Γ— 10⁹⁹(100-digit number)
17816851749098357895…60312164551970324481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.563 Γ— 10⁹⁹(100-digit number)
35633703498196715791…20624329103940648961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.126 Γ— 10⁹⁹(100-digit number)
71267406996393431582…41248658207881297921
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:57,720,595 XPMΒ·at block #6,809,564 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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