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Block #1,101,504

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/12/2015, 3:31:28 PM Β· Difficulty 10.7584 Β· 5,709,435 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
de7124358ddc3ab00239f5327530c72695eb69656135990728994d435acde698
View on Chainz β†—

Height

#1,101,504

Difficulty

10.758450

Transactions

1

Size

200 B

Version

2

Bits

0ac229c2

Nonce

47,236,027

Timestamp

6/12/2015, 3:31:28 PM

Confirmations

5,709,435

Mined by

⛏️ P2SHANCZAhFAbKSZQtiaCEE6qAhDsq4XJ8NSvi

Merkle Root

677bcdb1dae20fbc054374819ab56677e57351c24081f88eb498a777781d05ba
Transactions (1)
Coinbase677bcdb1dae20f…98a777781d05ba
1 in β†’ 1 out8.6300 XPM109 B
ANCZAhFA…4XJ8NSvi
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.

6.672 Γ— 10⁹⁢(97-digit number)
66726698013297662232…32255982816318951999
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
6.672 Γ— 10⁹⁢(97-digit number)
66726698013297662232…32255982816318951999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.334 Γ— 10⁹⁷(98-digit number)
13345339602659532446…64511965632637903999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.669 Γ— 10⁹⁷(98-digit number)
26690679205319064893…29023931265275807999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.338 Γ— 10⁹⁷(98-digit number)
53381358410638129786…58047862530551615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.067 Γ— 10⁹⁸(99-digit number)
10676271682127625957…16095725061103231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.135 Γ— 10⁹⁸(99-digit number)
21352543364255251914…32191450122206463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.270 Γ— 10⁹⁸(99-digit number)
42705086728510503829…64382900244412927999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.541 Γ— 10⁹⁸(99-digit number)
85410173457021007658…28765800488825855999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.708 Γ— 10⁹⁹(100-digit number)
17082034691404201531…57531600977651711999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.416 Γ— 10⁹⁹(100-digit number)
34164069382808403063…15063201955303423999
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:57,731,609 XPMΒ·at block #6,810,938 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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