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Block #2,133,683

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/26/2017, 5:04:24 PM Β· Difficulty 10.9092 Β· 4,707,470 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c60e0e63e23048bbc3cd5fb93437a44ad0a9e4c0c532a26f37e3346e2911b189
View on Chainz β†—

Height

#2,133,683

Difficulty

10.909185

Transactions

1

Size

200 B

Version

2

Bits

0ae8c05a

Nonce

1,363,197,811

Timestamp

5/26/2017, 5:04:24 PM

Confirmations

4,707,470

Mined by

⛏️ P2SHATbsg7ci6hyaKp1hbh6oeFbeckcMzTpWaz

Merkle Root

5d9e2126288dfbf776518b7a03e692be0b3391b30989f06db0c69dba7d5737f2
Transactions (1)
Coinbase5d9e2126288dfb…c69dba7d5737f2
1 in β†’ 1 out8.3900 XPM109 B
ATbsg7ci…cMzTpWaz
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.

9.809 Γ— 10⁹⁢(97-digit number)
98099196134606789783…00820927720207482879
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
9.809 Γ— 10⁹⁢(97-digit number)
98099196134606789783…00820927720207482879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.961 Γ— 10⁹⁷(98-digit number)
19619839226921357956…01641855440414965759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.923 Γ— 10⁹⁷(98-digit number)
39239678453842715913…03283710880829931519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.847 Γ— 10⁹⁷(98-digit number)
78479356907685431826…06567421761659863039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.569 Γ— 10⁹⁸(99-digit number)
15695871381537086365…13134843523319726079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.139 Γ— 10⁹⁸(99-digit number)
31391742763074172730…26269687046639452159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.278 Γ— 10⁹⁸(99-digit number)
62783485526148345461…52539374093278904319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.255 Γ— 10⁹⁹(100-digit number)
12556697105229669092…05078748186557808639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.511 Γ— 10⁹⁹(100-digit number)
25113394210459338184…10157496373115617279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.022 Γ— 10⁹⁹(100-digit number)
50226788420918676369…20314992746231234559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.004 Γ— 10¹⁰⁰(101-digit number)
10045357684183735273…40629985492462469119
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:57,973,587 XPMΒ·at block #6,841,152 Β· updates every 60s
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