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Block #2,268,628

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/26/2017, 9:18:43 AM Β· Difficulty 10.9525 Β· 4,568,136 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
589327dfd8b34b4f3886044c3af69139544214b213d8af1b5c18feac318d0a62
View on Chainz β†—

Height

#2,268,628

Difficulty

10.952487

Transactions

2

Size

1.17 KB

Version

2

Bits

0af3d628

Nonce

424,552,554

Timestamp

8/26/2017, 9:18:43 AM

Confirmations

4,568,136

Mined by

⛏️ P2SHAKhoLpK6MTMbu8JTCm5SNFeeFpJMJtmutB

Merkle Root

5c14641fc409facce973ec0b8fed3580e346cc6c025d4d279e170255bc87e396
Transactions (2)
Coinbase82182329df2fb6…4e64a3a41dd1bd
1 in β†’ 1 out8.3400 XPM110 B
AKhoLpK6…JMJtmutB
b60a68298140b4…6fc00834cb14f4
6 in β†’ 3 out2721.0339 XPM999 B
ASnzm9S9…A3PBVhJEAVipEwot…F1wirN7EARJ9NFbJ…2HGJTDJR
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.

5.187 Γ— 10⁹⁴(95-digit number)
51877845925729403432…04023189763405128561
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
5.187 Γ— 10⁹⁴(95-digit number)
51877845925729403432…04023189763405128561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.037 Γ— 10⁹⁡(96-digit number)
10375569185145880686…08046379526810257121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.075 Γ— 10⁹⁡(96-digit number)
20751138370291761373…16092759053620514241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.150 Γ— 10⁹⁡(96-digit number)
41502276740583522746…32185518107241028481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.300 Γ— 10⁹⁡(96-digit number)
83004553481167045492…64371036214482056961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.660 Γ— 10⁹⁢(97-digit number)
16600910696233409098…28742072428964113921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.320 Γ— 10⁹⁢(97-digit number)
33201821392466818196…57484144857928227841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.640 Γ— 10⁹⁢(97-digit number)
66403642784933636393…14968289715856455681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.328 Γ— 10⁹⁷(98-digit number)
13280728556986727278…29936579431712911361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.656 Γ— 10⁹⁷(98-digit number)
26561457113973454557…59873158863425822721
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,938,395 XPMΒ·at block #6,836,763 Β· updates every 60s
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