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Block #1,681,593

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2016, 10:57:49 AM Β· Difficulty 10.7162 Β· 5,160,630 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
31171d8782f03f9dbf45a742405ef3e1e2416c60e78886856e5643c86c82f9dd
View on Chainz β†—

Height

#1,681,593

Difficulty

10.716163

Transactions

1

Size

200 B

Version

2

Bits

0ab75675

Nonce

796,065,844

Timestamp

7/20/2016, 10:57:49 AM

Confirmations

5,160,630

Mined by

⛏️ P2SHAS3oiomxd1R2xpgCteu2bR7pcLSBXNg8Wp

Merkle Root

037a87372c8f61a28b71a17b639b9c1c89664639266c80dc7262f60bc74140d4
Transactions (1)
Coinbase037a87372c8f61…62f60bc74140d4
1 in β†’ 1 out8.6900 XPM109 B
AS3oiomx…SBXNg8Wp
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.

1.328 Γ— 10⁹⁢(97-digit number)
13281505823701089623…38209530902596485119
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
1.328 Γ— 10⁹⁢(97-digit number)
13281505823701089623…38209530902596485119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.656 Γ— 10⁹⁢(97-digit number)
26563011647402179246…76419061805192970239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.312 Γ— 10⁹⁢(97-digit number)
53126023294804358493…52838123610385940479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.062 Γ— 10⁹⁷(98-digit number)
10625204658960871698…05676247220771880959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.125 Γ— 10⁹⁷(98-digit number)
21250409317921743397…11352494441543761919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.250 Γ— 10⁹⁷(98-digit number)
42500818635843486794…22704988883087523839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.500 Γ— 10⁹⁷(98-digit number)
85001637271686973589…45409977766175047679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.700 Γ— 10⁹⁸(99-digit number)
17000327454337394717…90819955532350095359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.400 Γ— 10⁹⁸(99-digit number)
34000654908674789435…81639911064700190719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.800 Γ— 10⁹⁸(99-digit number)
68001309817349578871…63279822129400381439
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
Circulating Supply:57,982,182 XPMΒ·at block #6,842,222 Β· updates every 60s
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