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Block #1,169,023

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/25/2015, 12:40:16 AM Β· Difficulty 10.9353 Β· 5,675,807 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
180c7ef5aeeb3e7a0fed004f1aca3e341c6e917696b9b690d3062cb9d1f3678e
View on Chainz β†—

Height

#1,169,023

Difficulty

10.935257

Transactions

1

Size

200 B

Version

2

Bits

0aef6d03

Nonce

980,960,707

Timestamp

7/25/2015, 12:40:16 AM

Confirmations

5,675,807

Mined by

⛏️ P2SHAH2miipBLrknrjDYLD8qo5BPVixdUbQeCb

Merkle Root

ec2d79122ff73e73a1527e67d8d709c59c72a883f3ace00bae9158ee07f7e92f
Transactions (1)
Coinbaseec2d79122ff73e…9158ee07f7e92f
1 in β†’ 1 out8.3500 XPM110 B
AH2miipB…xdUbQeCb
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.

1.128 Γ— 10⁹⁴(95-digit number)
11288437343114686444…91560967184429842831
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
1.128 Γ— 10⁹⁴(95-digit number)
11288437343114686444…91560967184429842831
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.257 Γ— 10⁹⁴(95-digit number)
22576874686229372889…83121934368859685661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.515 Γ— 10⁹⁴(95-digit number)
45153749372458745779…66243868737719371321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.030 Γ— 10⁹⁴(95-digit number)
90307498744917491558…32487737475438742641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.806 Γ— 10⁹⁡(96-digit number)
18061499748983498311…64975474950877485281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.612 Γ— 10⁹⁡(96-digit number)
36122999497966996623…29950949901754970561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.224 Γ— 10⁹⁡(96-digit number)
72245998995933993246…59901899803509941121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.444 Γ— 10⁹⁢(97-digit number)
14449199799186798649…19803799607019882241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.889 Γ— 10⁹⁢(97-digit number)
28898399598373597298…39607599214039764481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.779 Γ— 10⁹⁢(97-digit number)
57796799196747194597…79215198428079528961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.155 Γ— 10⁹⁷(98-digit number)
11559359839349438919…58430396856159057921
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:58,003,049 XPMΒ·at block #6,844,829 Β· updates every 60s
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