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Block #851,868

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/13/2014, 3:16:26 PM Β· Difficulty 10.9704 Β· 5,993,114 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f045dd5e1ba63ec52e6e75474bb62011465a974b8f9a10a83c944dbcf0e5e1b1
View on Chainz β†—

Height

#851,868

Difficulty

10.970385

Transactions

2

Size

696 B

Version

2

Bits

0af86b21

Nonce

409,987,261

Timestamp

12/13/2014, 3:16:26 PM

Confirmations

5,993,114

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7aa04594be45b5ac14c44d4f8fa1634a1d13fb084fcd524135c2a11044bd46a1
Transactions (2)
Coinbase7edb59a634824e…1231c0dc8ac039
1 in β†’ 1 out8.3199 XPM116 B
ANSXnLY2…Sd25TjkD
255fe7352cb60e…7b519b1ad9c905
3 in β†’ 1 out0.0111 XPM490 B
AJarDrFr…JYKnEaRA
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.

2.852 Γ— 10⁹⁡(96-digit number)
28525919315141414333…83171654413924238011
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
2.852 Γ— 10⁹⁡(96-digit number)
28525919315141414333…83171654413924238011
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.705 Γ— 10⁹⁡(96-digit number)
57051838630282828666…66343308827848476021
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.141 Γ— 10⁹⁢(97-digit number)
11410367726056565733…32686617655696952041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.282 Γ— 10⁹⁢(97-digit number)
22820735452113131466…65373235311393904081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.564 Γ— 10⁹⁢(97-digit number)
45641470904226262933…30746470622787808161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.128 Γ— 10⁹⁢(97-digit number)
91282941808452525866…61492941245575616321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.825 Γ— 10⁹⁷(98-digit number)
18256588361690505173…22985882491151232641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.651 Γ— 10⁹⁷(98-digit number)
36513176723381010346…45971764982302465281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.302 Γ— 10⁹⁷(98-digit number)
73026353446762020693…91943529964604930561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.460 Γ— 10⁹⁸(99-digit number)
14605270689352404138…83887059929209861121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.921 Γ— 10⁹⁸(99-digit number)
29210541378704808277…67774119858419722241
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
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