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Block #2,113,540

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/13/2017, 1:30:50 AM Β· Difficulty 10.8992 Β· 4,727,994 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b8319e119c93bdc58ee7ba5fe5a6f08e278e59a5e404ee02f448fc65e43faa61
View on Chainz β†—

Height

#2,113,540

Difficulty

10.899217

Transactions

2

Size

391 B

Version

2

Bits

0ae6331e

Nonce

186,284,089

Timestamp

5/13/2017, 1:30:50 AM

Confirmations

4,727,994

Mined by

⛏️ P2SHANud3o2CLafUm8J5JCyE4o4H4aDERoBFq3

Merkle Root

dc7db770d6235816b76d3100b04dfe613faf25a93387db2432e2759f98008f99
Transactions (2)
Coinbase4f552c7781f537…a24f7ce5e84f29
1 in β†’ 1 out8.4100 XPM110 B
ANud3o2C…DERoBFq3
4d50ad79867d33…3efd5c0253a05b
1 in β†’ 1 out1928.4100 XPM191 B
AJmtAkFb…3LPR3CNx
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.

6.102 Γ— 10⁹⁡(96-digit number)
61021820147195393806…87608703595308486399
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
6.102 Γ— 10⁹⁡(96-digit number)
61021820147195393806…87608703595308486399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.220 Γ— 10⁹⁢(97-digit number)
12204364029439078761…75217407190616972799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.440 Γ— 10⁹⁢(97-digit number)
24408728058878157522…50434814381233945599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.881 Γ— 10⁹⁢(97-digit number)
48817456117756315044…00869628762467891199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.763 Γ— 10⁹⁢(97-digit number)
97634912235512630089…01739257524935782399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.952 Γ— 10⁹⁷(98-digit number)
19526982447102526017…03478515049871564799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.905 Γ— 10⁹⁷(98-digit number)
39053964894205052035…06957030099743129599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.810 Γ— 10⁹⁷(98-digit number)
78107929788410104071…13914060199486259199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.562 Γ— 10⁹⁸(99-digit number)
15621585957682020814…27828120398972518399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.124 Γ— 10⁹⁸(99-digit number)
31243171915364041628…55656240797945036799
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:57,976,655 XPMΒ·at block #6,841,533 Β· updates every 60s
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