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Block #1,086,318

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/2/2015, 4:31:35 AM Β· Difficulty 10.7518 Β· 5,723,459 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7c8e119dd3309998b6561fdf1e91941b3123568700330d2d36f1df2d4b2a9c0f
View on Chainz β†—

Height

#1,086,318

Difficulty

10.751801

Transactions

1

Size

200 B

Version

2

Bits

0ac0760a

Nonce

34,656,639

Timestamp

6/2/2015, 4:31:35 AM

Confirmations

5,723,459

Mined by

⛏️ P2SHANCZAhFAbKSZQtiaCEE6qAhDsq4XJ8NSvi

Merkle Root

28549c3148eea793c40fed197479da79ac3dfa505bdfc1aeec4139a166da2692
Transactions (1)
Coinbase28549c3148eea7…4139a166da2692
1 in β†’ 1 out8.6400 XPM109 B
ANCZAhFA…4XJ8NSvi
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.

1.857 Γ— 10⁹⁸(99-digit number)
18578535350951341503…37483681115881144321
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
1.857 Γ— 10⁹⁸(99-digit number)
18578535350951341503…37483681115881144321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.715 Γ— 10⁹⁸(99-digit number)
37157070701902683006…74967362231762288641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.431 Γ— 10⁹⁸(99-digit number)
74314141403805366013…49934724463524577281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.486 Γ— 10⁹⁹(100-digit number)
14862828280761073202…99869448927049154561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.972 Γ— 10⁹⁹(100-digit number)
29725656561522146405…99738897854098309121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.945 Γ— 10⁹⁹(100-digit number)
59451313123044292810…99477795708196618241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.189 Γ— 10¹⁰⁰(101-digit number)
11890262624608858562…98955591416393236481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.378 Γ— 10¹⁰⁰(101-digit number)
23780525249217717124…97911182832786472961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.756 Γ— 10¹⁰⁰(101-digit number)
47561050498435434248…95822365665572945921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.512 Γ— 10¹⁰⁰(101-digit number)
95122100996870868496…91644731331145891841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.902 Γ— 10¹⁰¹(102-digit number)
19024420199374173699…83289462662291783681
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:57,722,302 XPMΒ·at block #6,809,776 Β· updates every 60s
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