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Block #1,134,290

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/30/2015, 3:51:52 PM Β· Difficulty 10.9386 Β· 5,678,739 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
15cef9f2edaed68eb8a3bf49760455e75b6b082713e3e22f016c798f33461077
View on Chainz β†—

Height

#1,134,290

Difficulty

10.938611

Transactions

2

Size

724 B

Version

2

Bits

0af048ca

Nonce

141,667,670

Timestamp

6/30/2015, 3:51:52 PM

Confirmations

5,678,739

Mined by

⛏️ P2SHAdfpXYZfXgDfBVm66dqo4xtYvC7yAcreHH

Merkle Root

cd15d3fb82137de202ceffa646d1832fc5076c2104a5f0d06b2aa5c4a02c41f3
Transactions (2)
Coinbasee0ebb6dbdb0c82…464d22ba30a199
1 in β†’ 1 out8.3500 XPM109 B
AdfpXYZf…7yAcreHH
de637fa558a336…48c7db166d40b1
3 in β†’ 2 out3.6387 XPM524 B
AK9LxQQh…h24pctRmAeCahvq1…fJ5XbXvE
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.

9.937 Γ— 10⁹⁡(96-digit number)
99377240915436832987…67849006233080252161
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
9.937 Γ— 10⁹⁡(96-digit number)
99377240915436832987…67849006233080252161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.987 Γ— 10⁹⁢(97-digit number)
19875448183087366597…35698012466160504321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.975 Γ— 10⁹⁢(97-digit number)
39750896366174733195…71396024932321008641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.950 Γ— 10⁹⁢(97-digit number)
79501792732349466390…42792049864642017281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.590 Γ— 10⁹⁷(98-digit number)
15900358546469893278…85584099729284034561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.180 Γ— 10⁹⁷(98-digit number)
31800717092939786556…71168199458568069121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.360 Γ— 10⁹⁷(98-digit number)
63601434185879573112…42336398917136138241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.272 Γ— 10⁹⁸(99-digit number)
12720286837175914622…84672797834272276481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.544 Γ— 10⁹⁸(99-digit number)
25440573674351829244…69345595668544552961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.088 Γ— 10⁹⁸(99-digit number)
50881147348703658489…38691191337089105921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.017 Γ— 10⁹⁹(100-digit number)
10176229469740731697…77382382674178211841
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:57,748,274 XPMΒ·at block #6,813,028 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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