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Block #787,715

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/29/2014, 6:26:44 AM Β· Difficulty 10.9745 Β· 6,015,846 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c011adada4b0f1883d47ac35c22996a1996de162a72255e2abd4414bd0140fde
View on Chainz β†—

Height

#787,715

Difficulty

10.974543

Transactions

2

Size

21.38 KB

Version

2

Bits

0af97ba3

Nonce

1,208,371,434

Timestamp

10/29/2014, 6:26:44 AM

Confirmations

6,015,846

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

97f3695675b87f64bed95a383427cd7d3078c7af7126dcf9fc911463c1606fe1
Transactions (2)
Coinbasea50a17a8db0f88…43a287647f33c6
1 in β†’ 1 out8.5300 XPM116 B
ANSXnLY2…Sd25TjkD
28c317e75dbcd5…9db9bb5da67d12
146 in β†’ 2 out20000.0100 XPM21.18 KB
ATNFg4tq…AMdaKJFHAcjMzXyj…sd2B5Pqn
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.

1.339 Γ— 10⁹⁷(98-digit number)
13391972914863114902…22290914601920206081
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
1.339 Γ— 10⁹⁷(98-digit number)
13391972914863114902…22290914601920206081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.678 Γ— 10⁹⁷(98-digit number)
26783945829726229805…44581829203840412161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.356 Γ— 10⁹⁷(98-digit number)
53567891659452459610…89163658407680824321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.071 Γ— 10⁹⁸(99-digit number)
10713578331890491922…78327316815361648641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.142 Γ— 10⁹⁸(99-digit number)
21427156663780983844…56654633630723297281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.285 Γ— 10⁹⁸(99-digit number)
42854313327561967688…13309267261446594561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.570 Γ— 10⁹⁸(99-digit number)
85708626655123935376…26618534522893189121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.714 Γ— 10⁹⁹(100-digit number)
17141725331024787075…53237069045786378241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.428 Γ— 10⁹⁹(100-digit number)
34283450662049574150…06474138091572756481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.856 Γ— 10⁹⁹(100-digit number)
68566901324099148301…12948276183145512961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.371 Γ— 10¹⁰⁰(101-digit number)
13713380264819829660…25896552366291025921
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:57,672,520 XPMΒ·at block #6,803,560 Β· updates every 60s
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