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Block #2,650,363

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/5/2018, 11:57:02 PM Β· Difficulty 11.7571 Β· 4,187,675 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
66c99bc0a103b9f4a523498ae85011efd81026d0e354d47e999fa91e7cc4b6cc
View on Chainz β†—

Height

#2,650,363

Difficulty

11.757116

Transactions

2

Size

540 B

Version

2

Bits

0bc1d25a

Nonce

166,843,911

Timestamp

5/5/2018, 11:57:02 PM

Confirmations

4,187,675

Mined by

⛏️ P2SHAFoK8YAVbgSj9RmpxEpyoQqnaWon2iw2ug

Merkle Root

c16eb7ee5ad4d11cf26d285c1d331ec1dc2373810d31e3c78c05198cb491f52f
Transactions (2)
Coinbase70db73d5bf3968…e05f0581125b1a
1 in β†’ 1 out7.2300 XPM110 B
AFoK8YAV…on2iw2ug
54e3331ee1af2a…e6b893eb25e5da
2 in β†’ 1 out2499.9900 XPM340 B
AGq2Nru3…2dvKMDay
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.

1.165 Γ— 10⁹⁡(96-digit number)
11659122576127991398…84814850590306165441
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.165 Γ— 10⁹⁡(96-digit number)
11659122576127991398…84814850590306165441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.331 Γ— 10⁹⁡(96-digit number)
23318245152255982797…69629701180612330881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.663 Γ— 10⁹⁡(96-digit number)
46636490304511965595…39259402361224661761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.327 Γ— 10⁹⁡(96-digit number)
93272980609023931190…78518804722449323521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.865 Γ— 10⁹⁢(97-digit number)
18654596121804786238…57037609444898647041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.730 Γ— 10⁹⁢(97-digit number)
37309192243609572476…14075218889797294081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.461 Γ— 10⁹⁢(97-digit number)
74618384487219144952…28150437779594588161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.492 Γ— 10⁹⁷(98-digit number)
14923676897443828990…56300875559189176321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.984 Γ— 10⁹⁷(98-digit number)
29847353794887657980…12601751118378352641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.969 Γ— 10⁹⁷(98-digit number)
59694707589775315961…25203502236756705281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.193 Γ— 10⁹⁸(99-digit number)
11938941517955063192…50407004473513410561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
2.387 Γ— 10⁹⁸(99-digit number)
23877883035910126384…00814008947026821121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the Second 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,948,655 XPMΒ·at block #6,838,037 Β· updates every 60s
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