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Block #1,366,175

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/12/2015, 3:45:21 AM Β· Difficulty 10.8445 Β· 5,440,737 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
07c0ba44de9bb2b37dd2ac132af8a8a32f9e9d5f5c7fd67ff0ff1a7dd056878a
View on Chainz β†—

Height

#1,366,175

Difficulty

10.844465

Transactions

2

Size

3.02 KB

Version

2

Bits

0ad82ed7

Nonce

487,761,573

Timestamp

12/12/2015, 3:45:21 AM

Confirmations

5,440,737

Mined by

⛏️ P2SHAFpy4Gycz2qaNcVQYPk42GP2qD7YpNQGpf

Merkle Root

ec148c760f145be479dfe895b25496268573d795af3429696f6dfcba3046f709
Transactions (2)
Coinbase7f55dd309a19cc…d8b2be3fa85162
1 in β†’ 1 out8.5800 XPM109 B
AFpy4Gyc…7YpNQGpf
204144e74f4d93…97db35cc6e8783
19 in β†’ 2 out1393.0000 XPM2.82 KB
AbDs3Ren…RsC3PTA7AHNccZy4…RwZSfQd3
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.

1.467 Γ— 10⁹⁡(96-digit number)
14677212768602682718…68174523048842045441
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
1.467 Γ— 10⁹⁡(96-digit number)
14677212768602682718…68174523048842045441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.935 Γ— 10⁹⁡(96-digit number)
29354425537205365437…36349046097684090881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.870 Γ— 10⁹⁡(96-digit number)
58708851074410730874…72698092195368181761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.174 Γ— 10⁹⁢(97-digit number)
11741770214882146174…45396184390736363521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.348 Γ— 10⁹⁢(97-digit number)
23483540429764292349…90792368781472727041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.696 Γ— 10⁹⁢(97-digit number)
46967080859528584699…81584737562945454081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.393 Γ— 10⁹⁢(97-digit number)
93934161719057169398…63169475125890908161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.878 Γ— 10⁹⁷(98-digit number)
18786832343811433879…26338950251781816321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.757 Γ— 10⁹⁷(98-digit number)
37573664687622867759…52677900503563632641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.514 Γ— 10⁹⁷(98-digit number)
75147329375245735518…05355801007127265281
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:57,699,399 XPMΒ·at block #6,806,911 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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