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Block #2,634,076

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 6:14:13 PM Β· Difficulty 11.2213 Β· 4,196,808 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
270486459e8a0bf35b519429141b2f94d2f3a29231120128797c8002dc31e7cb
View on Chainz β†—

Height

#2,634,076

Difficulty

11.221283

Transactions

2

Size

427 B

Version

2

Bits

0b38a5ff

Nonce

1,320,308,134

Timestamp

4/28/2018, 6:14:13 PM

Confirmations

4,196,808

Mined by

⛏️ P2SHAM7hd5hNTAudEQsYaVHwGFvW2sfWTJgakn

Merkle Root

2d4241a16ae3e081a297fd550d5ef98b5905f8e8ac0fdfd6b31fba8d264c2505
Transactions (2)
Coinbasea730f6728c5202…5f99277db8e7eb
1 in β†’ 1 out7.9400 XPM110 B
AM7hd5hN…fWTJgakn
a9d85733a7b446…2286dcd7ed9b63
1 in β†’ 2 out1.3320 XPM227 B
AVhXa3fj…Y6pzurwkARd3BL3F…WhiJV6e5
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.

9.364 Γ— 10⁹⁴(95-digit number)
93641735908089227742…59722654825250150761
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
9.364 Γ— 10⁹⁴(95-digit number)
93641735908089227742…59722654825250150761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.872 Γ— 10⁹⁡(96-digit number)
18728347181617845548…19445309650500301521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.745 Γ— 10⁹⁡(96-digit number)
37456694363235691096…38890619301000603041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.491 Γ— 10⁹⁡(96-digit number)
74913388726471382193…77781238602001206081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.498 Γ— 10⁹⁢(97-digit number)
14982677745294276438…55562477204002412161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.996 Γ— 10⁹⁢(97-digit number)
29965355490588552877…11124954408004824321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.993 Γ— 10⁹⁢(97-digit number)
59930710981177105754…22249908816009648641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.198 Γ— 10⁹⁷(98-digit number)
11986142196235421150…44499817632019297281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.397 Γ— 10⁹⁷(98-digit number)
23972284392470842301…88999635264038594561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.794 Γ— 10⁹⁷(98-digit number)
47944568784941684603…77999270528077189121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.588 Γ— 10⁹⁷(98-digit number)
95889137569883369207…55998541056154378241
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:57,891,208 XPMΒ·at block #6,830,883 Β· updates every 60s
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