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Block #1,680,837

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/19/2016, 11:51:03 PM Β· Difficulty 10.7111 Β· 5,160,992 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7ec0cb20ff369cd332a90937a66501ea28bd7457336f171b6558e55fc31913e1
View on Chainz β†—

Height

#1,680,837

Difficulty

10.711132

Transactions

1

Size

200 B

Version

2

Bits

0ab60cbe

Nonce

1,249,180,546

Timestamp

7/19/2016, 11:51:03 PM

Confirmations

5,160,992

Mined by

⛏️ P2SHAc6wrPG4cXhp4Zcsq4hDWrkxyKKkjCyiDV

Merkle Root

5cd12e5c125795280f17c451b0c15f7f017d7c75a3573c08ab0a1d204e5bfd39
Transactions (1)
Coinbase5cd12e5c125795…0a1d204e5bfd39
1 in β†’ 1 out8.7000 XPM109 B
Ac6wrPG4…KkjCyiDV
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.

1.056 Γ— 10⁹⁢(97-digit number)
10568233757382317063…67268233232825978879
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
1.056 Γ— 10⁹⁢(97-digit number)
10568233757382317063…67268233232825978879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.113 Γ— 10⁹⁢(97-digit number)
21136467514764634127…34536466465651957759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.227 Γ— 10⁹⁢(97-digit number)
42272935029529268254…69072932931303915519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.454 Γ— 10⁹⁢(97-digit number)
84545870059058536509…38145865862607831039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.690 Γ— 10⁹⁷(98-digit number)
16909174011811707301…76291731725215662079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.381 Γ— 10⁹⁷(98-digit number)
33818348023623414603…52583463450431324159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.763 Γ— 10⁹⁷(98-digit number)
67636696047246829207…05166926900862648319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.352 Γ— 10⁹⁸(99-digit number)
13527339209449365841…10333853801725296639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.705 Γ— 10⁹⁸(99-digit number)
27054678418898731683…20667707603450593279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.410 Γ— 10⁹⁸(99-digit number)
54109356837797463366…41335415206901186559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.082 Γ— 10⁹⁹(100-digit number)
10821871367559492673…82670830413802373119
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:57,979,005 XPMΒ·at block #6,841,828 Β· updates every 60s
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