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Block #1,680,841

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/19/2016, 11:54:52 PM Β· Difficulty 10.7111 Β· 5,159,674 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b4a7c9546695926dde73bfcb4fdd3454c0c777869a9b366183e288e372fe3073
View on Chainz β†—

Height

#1,680,841

Difficulty

10.711124

Transactions

1

Size

199 B

Version

2

Bits

0ab60c40

Nonce

703,008,909

Timestamp

7/19/2016, 11:54:52 PM

Confirmations

5,159,674

Mined by

⛏️ P2SHAVfdWPv987qxBoovRHV3PRTrfHBabksQhw

Merkle Root

c8d58204e2abd5686e34d2a960692a626e58dce7919a0ec382fa06f35fac0f74
Transactions (1)
Coinbasec8d58204e2abd5…fa06f35fac0f74
1 in β†’ 1 out8.7000 XPM109 B
AVfdWPv9…BabksQhw
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.

5.797 Γ— 10⁹⁴(95-digit number)
57971687338414368058…78138258682637819359
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
5.797 Γ— 10⁹⁴(95-digit number)
57971687338414368058…78138258682637819359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.159 Γ— 10⁹⁡(96-digit number)
11594337467682873611…56276517365275638719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.318 Γ— 10⁹⁡(96-digit number)
23188674935365747223…12553034730551277439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.637 Γ— 10⁹⁡(96-digit number)
46377349870731494446…25106069461102554879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.275 Γ— 10⁹⁡(96-digit number)
92754699741462988893…50212138922205109759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.855 Γ— 10⁹⁢(97-digit number)
18550939948292597778…00424277844410219519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.710 Γ— 10⁹⁢(97-digit number)
37101879896585195557…00848555688820439039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.420 Γ— 10⁹⁢(97-digit number)
74203759793170391114…01697111377640878079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.484 Γ— 10⁹⁷(98-digit number)
14840751958634078222…03394222755281756159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.968 Γ— 10⁹⁷(98-digit number)
29681503917268156445…06788445510563512319
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:57,968,448 XPMΒ·at block #6,840,514 Β· updates every 60s
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