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Block #1,192,086

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/12/2015, 6:29:24 PM Β· Difficulty 10.8602 Β· 5,649,848 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
55f103419c91a0d88008fbac0b6d7a907bcfd69e79d08248a61eba95cd07b953
View on Chainz β†—

Height

#1,192,086

Difficulty

10.860227

Transactions

2

Size

9.97 KB

Version

2

Bits

0adc37d9

Nonce

1,675,144,971

Timestamp

8/12/2015, 6:29:24 PM

Confirmations

5,649,848

Mined by

⛏️ P2SHAT52KcPgHFW9xaYuHJTduP4H4pZ2ytw2iY

Merkle Root

e539191aa2b1630628e3c6ae11e6aad2bf16025c44f90da76a4fa09c19717b38
Transactions (2)
Coinbase3d6c3ee8c6f7b2…7ab4f15a6a31fb
1 in β†’ 1 out8.5900 XPM109 B
AT52KcPg…Z2ytw2iY
a2804152bac684…9d97bdee25923d
67 in β†’ 2 out286.5528 XPM9.77 KB
AYeGLxtJ…3XFCDFMmAJdUfky5…Mzu24Ua2
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.

4.263 Γ— 10⁹³(94-digit number)
42639493416288205385…75590042464932947841
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
4.263 Γ— 10⁹³(94-digit number)
42639493416288205385…75590042464932947841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.527 Γ— 10⁹³(94-digit number)
85278986832576410771…51180084929865895681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.705 Γ— 10⁹⁴(95-digit number)
17055797366515282154…02360169859731791361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.411 Γ— 10⁹⁴(95-digit number)
34111594733030564308…04720339719463582721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.822 Γ— 10⁹⁴(95-digit number)
68223189466061128616…09440679438927165441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.364 Γ— 10⁹⁡(96-digit number)
13644637893212225723…18881358877854330881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.728 Γ— 10⁹⁡(96-digit number)
27289275786424451446…37762717755708661761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.457 Γ— 10⁹⁡(96-digit number)
54578551572848902893…75525435511417323521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.091 Γ— 10⁹⁢(97-digit number)
10915710314569780578…51050871022834647041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.183 Γ— 10⁹⁢(97-digit number)
21831420629139561157…02101742045669294081
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,979,851 XPMΒ·at block #6,841,933 Β· updates every 60s
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