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Block #839,812

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/4/2014, 4:44:45 PM Β· Difficulty 10.9745 Β· 6,001,743 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0bed2f2a3eb9e2e013ca812cee9b0d0579c4a2002b9132c643bfd9f49aea65c0
View on Chainz β†—

Height

#839,812

Difficulty

10.974467

Transactions

2

Size

432 B

Version

2

Bits

0af976ac

Nonce

286,348,401

Timestamp

12/4/2014, 4:44:45 PM

Confirmations

6,001,743

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

44016060fcec77b3a7d36fc49d30a120472975dbce1fa4178616babd67328ffe
Transactions (2)
Coinbased43d805f1c3ab6…9c359664d396d6
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
4135f55b516dc4…bd640afe4f6dec
1 in β†’ 2 out0.3954 XPM226 B
AY7mvy48…Ua1vrwEPANo8jKhF…Pm6nJEpb
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.

7.508 Γ— 10⁹⁡(96-digit number)
75085394622375296829…53904923085500772001
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
7.508 Γ— 10⁹⁡(96-digit number)
75085394622375296829…53904923085500772001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.501 Γ— 10⁹⁢(97-digit number)
15017078924475059365…07809846171001544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.003 Γ— 10⁹⁢(97-digit number)
30034157848950118731…15619692342003088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.006 Γ— 10⁹⁢(97-digit number)
60068315697900237463…31239384684006176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.201 Γ— 10⁹⁷(98-digit number)
12013663139580047492…62478769368012352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.402 Γ— 10⁹⁷(98-digit number)
24027326279160094985…24957538736024704001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.805 Γ— 10⁹⁷(98-digit number)
48054652558320189970…49915077472049408001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.610 Γ— 10⁹⁷(98-digit number)
96109305116640379941…99830154944098816001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.922 Γ— 10⁹⁸(99-digit number)
19221861023328075988…99660309888197632001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.844 Γ— 10⁹⁸(99-digit number)
38443722046656151976…99320619776395264001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.688 Γ— 10⁹⁸(99-digit number)
76887444093312303953…98641239552790528001
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:57,976,825 XPMΒ·at block #6,841,554 Β· updates every 60s
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