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Block #740,011

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/25/2014, 4:21:55 AM Β· Difficulty 10.9794 Β· 6,070,822 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9fa01e70d0e4a4669beb85cb4d51540dc8824bde52a74e4b0fef8ac61e499685
View on Chainz β†—

Height

#740,011

Difficulty

10.979355

Transactions

2

Size

2.59 KB

Version

2

Bits

0afab709

Nonce

5,748,070

Timestamp

9/25/2014, 4:21:55 AM

Confirmations

6,070,822

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d608a4712b1cc396c3dabb8ecc060bc41e5a44d6168dc6a0ed9f34f60e35b6c7
Transactions (2)
Coinbase43d9b42813d366…d6660cbeac2375
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
12186512a2f935…a928a0d8f9c79e
16 in β†’ 2 out100.0161 XPM2.39 KB
APPBcNJi…a8d4PbipAYvZ7MYf…DCRLX5Q5
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.

1.674 Γ— 10⁹⁷(98-digit number)
16745848887359759330…34419094647196419839
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
1.674 Γ— 10⁹⁷(98-digit number)
16745848887359759330…34419094647196419839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.349 Γ— 10⁹⁷(98-digit number)
33491697774719518660…68838189294392839679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.698 Γ— 10⁹⁷(98-digit number)
66983395549439037321…37676378588785679359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.339 Γ— 10⁹⁸(99-digit number)
13396679109887807464…75352757177571358719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.679 Γ— 10⁹⁸(99-digit number)
26793358219775614928…50705514355142717439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.358 Γ— 10⁹⁸(99-digit number)
53586716439551229857…01411028710285434879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.071 Γ— 10⁹⁹(100-digit number)
10717343287910245971…02822057420570869759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.143 Γ— 10⁹⁹(100-digit number)
21434686575820491942…05644114841141739519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.286 Γ— 10⁹⁹(100-digit number)
42869373151640983885…11288229682283479039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.573 Γ— 10⁹⁹(100-digit number)
85738746303281967771…22576459364566958079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.714 Γ— 10¹⁰⁰(101-digit number)
17147749260656393554…45152918729133916159
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,730,759 XPMΒ·at block #6,810,832 Β· updates every 60s
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