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Block #2,634,781

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 12:39:04 AM Β· Difficulty 11.2693 Β· 4,205,870 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ad8eff3ca568bc79389269bef2b783dfedfe3969bc6de19eb244bcb3383e0a7a
View on Chainz β†—

Height

#2,634,781

Difficulty

11.269281

Transactions

1

Size

199 B

Version

2

Bits

0b44efa0

Nonce

1,835,889,500

Timestamp

4/29/2018, 12:39:04 AM

Confirmations

4,205,870

Mined by

⛏️ P2SHAHJxhwwFRJQUyQF2h7Uu8kNEeHZWQPK7ev

Merkle Root

df33c664957b49b6f19b394840f98195626dcfed40a32a439e8f373796c60495
Transactions (1)
Coinbasedf33c664957b49…8f373796c60495
1 in β†’ 1 out7.8600 XPM109 B
AHJxhwwF…ZWQPK7ev
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.

8.355 Γ— 10⁹⁡(96-digit number)
83552288321103373474…17394420218547443361
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
8.355 Γ— 10⁹⁡(96-digit number)
83552288321103373474…17394420218547443361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.671 Γ— 10⁹⁢(97-digit number)
16710457664220674694…34788840437094886721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.342 Γ— 10⁹⁢(97-digit number)
33420915328441349389…69577680874189773441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.684 Γ— 10⁹⁢(97-digit number)
66841830656882698779…39155361748379546881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.336 Γ— 10⁹⁷(98-digit number)
13368366131376539755…78310723496759093761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.673 Γ— 10⁹⁷(98-digit number)
26736732262753079511…56621446993518187521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.347 Γ— 10⁹⁷(98-digit number)
53473464525506159023…13242893987036375041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.069 Γ— 10⁹⁸(99-digit number)
10694692905101231804…26485787974072750081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.138 Γ— 10⁹⁸(99-digit number)
21389385810202463609…52971575948145500161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.277 Γ— 10⁹⁸(99-digit number)
42778771620404927218…05943151896291000321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.555 Γ— 10⁹⁸(99-digit number)
85557543240809854437…11886303792582000641
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:57,969,551 XPMΒ·at block #6,840,650 Β· updates every 60s
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