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Block #2,738,637

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/7/2018, 10:11:42 PM Β· Difficulty 11.6171 Β· 4,101,629 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b518dc7414be4768ff23e6fe528a9bbbf18b42ddfb102b049e8166a1b198a857
View on Chainz β†—

Height

#2,738,637

Difficulty

11.617142

Transactions

2

Size

10.96 KB

Version

2

Bits

0b9dfd09

Nonce

1,709,453,442

Timestamp

7/7/2018, 10:11:42 PM

Confirmations

4,101,629

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

2ebb9ac23f677491ca1e4d672bff9c82816e4b931b02b7fe264d4b001fda2bb1
Transactions (2)
Coinbasec95698cf283787…11bdf9223c2f53
1 in β†’ 1 out7.5200 XPM110 B
AZtxQr2F…7grUWrUz
d590e602823351…81051f4222b295
74 in β†’ 2 out295.8800 XPM10.76 KB
AXLvhvQ7…oY2kjnZXAQRn6yfR…z5FsKtdj
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.

3.544 Γ— 10⁹⁴(95-digit number)
35449619772348871302…52860489886724207361
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
3.544 Γ— 10⁹⁴(95-digit number)
35449619772348871302…52860489886724207361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.089 Γ— 10⁹⁴(95-digit number)
70899239544697742605…05720979773448414721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.417 Γ— 10⁹⁡(96-digit number)
14179847908939548521…11441959546896829441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.835 Γ— 10⁹⁡(96-digit number)
28359695817879097042…22883919093793658881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.671 Γ— 10⁹⁡(96-digit number)
56719391635758194084…45767838187587317761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.134 Γ— 10⁹⁢(97-digit number)
11343878327151638816…91535676375174635521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.268 Γ— 10⁹⁢(97-digit number)
22687756654303277633…83071352750349271041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.537 Γ— 10⁹⁢(97-digit number)
45375513308606555267…66142705500698542081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.075 Γ— 10⁹⁢(97-digit number)
90751026617213110535…32285411001397084161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.815 Γ— 10⁹⁷(98-digit number)
18150205323442622107…64570822002794168321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.630 Γ— 10⁹⁷(98-digit number)
36300410646885244214…29141644005588336641
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,966,442 XPMΒ·at block #6,840,265 Β· updates every 60s
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