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Block #713,214

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/9/2014, 4:00:16 AM Β· Difficulty 10.9556 Β· 6,117,670 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
86d465cf6a8e2cb9a18471c22a10604ee403b6bd7fe094f4af4e991210d0b4da
View on Chainz β†—

Height

#713,214

Difficulty

10.955606

Transactions

2

Size

581 B

Version

2

Bits

0af4a2a0

Nonce

237,620,572

Timestamp

9/9/2014, 4:00:16 AM

Confirmations

6,117,670

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

dc8f2f3668b40ea9c93bc381cec64887c15dc3dd5794d813333b108e41b4527f
Transactions (2)
Coinbasef866421a50a710…c55e9b6a884510
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
31781b4f3acde1…aca8bddbc4e8ac
2 in β†’ 2 out2079.9030 XPM374 B
ARseQQ6A…RPh9BxYPAVA1RjU2…Q9xB5waV
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.

6.518 Γ— 10⁹⁡(96-digit number)
65180204461788110599…83860017408079028479
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
6.518 Γ— 10⁹⁡(96-digit number)
65180204461788110599…83860017408079028479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.303 Γ— 10⁹⁢(97-digit number)
13036040892357622119…67720034816158056959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.607 Γ— 10⁹⁢(97-digit number)
26072081784715244239…35440069632316113919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.214 Γ— 10⁹⁢(97-digit number)
52144163569430488479…70880139264632227839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.042 Γ— 10⁹⁷(98-digit number)
10428832713886097695…41760278529264455679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.085 Γ— 10⁹⁷(98-digit number)
20857665427772195391…83520557058528911359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.171 Γ— 10⁹⁷(98-digit number)
41715330855544390783…67041114117057822719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.343 Γ— 10⁹⁷(98-digit number)
83430661711088781567…34082228234115645439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.668 Γ— 10⁹⁸(99-digit number)
16686132342217756313…68164456468231290879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.337 Γ— 10⁹⁸(99-digit number)
33372264684435512627…36328912936462581759
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
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