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Block #1,727,208

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/21/2016, 8:01:49 AM Β· Difficulty 10.7011 Β· 5,113,929 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c92218ccd794b3e642fcb8a71dc6706ba13034494b7d902049795b3b71e04b22
View on Chainz β†—

Height

#1,727,208

Difficulty

10.701075

Transactions

1

Size

200 B

Version

2

Bits

0ab379a8

Nonce

499,685,787

Timestamp

8/21/2016, 8:01:49 AM

Confirmations

5,113,929

Mined by

⛏️ P2SHARFngUL4ChBUCKiiJR4cWGy6xD1yg7zcjM

Merkle Root

be52e3ad9abde49f608d715a3c832e4924472bd3f2a96bd628dbf82de4affc37
Transactions (1)
Coinbasebe52e3ad9abde4…dbf82de4affc37
1 in β†’ 1 out8.7200 XPM109 B
ARFngUL4…1yg7zcjM
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.

3.415 Γ— 10⁹⁢(97-digit number)
34157744959236863917…71710451391758776319
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
3.415 Γ— 10⁹⁢(97-digit number)
34157744959236863917…71710451391758776319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.831 Γ— 10⁹⁢(97-digit number)
68315489918473727834…43420902783517552639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.366 Γ— 10⁹⁷(98-digit number)
13663097983694745566…86841805567035105279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.732 Γ— 10⁹⁷(98-digit number)
27326195967389491133…73683611134070210559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.465 Γ— 10⁹⁷(98-digit number)
54652391934778982267…47367222268140421119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.093 Γ— 10⁹⁸(99-digit number)
10930478386955796453…94734444536280842239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.186 Γ— 10⁹⁸(99-digit number)
21860956773911592907…89468889072561684479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.372 Γ— 10⁹⁸(99-digit number)
43721913547823185814…78937778145123368959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.744 Γ— 10⁹⁸(99-digit number)
87443827095646371628…57875556290246737919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.748 Γ— 10⁹⁹(100-digit number)
17488765419129274325…15751112580493475839
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:57,973,458 XPMΒ·at block #6,841,136 Β· updates every 60s
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