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Block #841,772

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/6/2014, 3:16:44 AM Β· Difficulty 10.9740 Β· 5,992,082 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5bf4cf59ec30a073328b0fee9764d4c35830913bea686d4d6e52964ff62f5607
View on Chainz β†—

Height

#841,772

Difficulty

10.973953

Transactions

2

Size

433 B

Version

2

Bits

0af95504

Nonce

248,697,341

Timestamp

12/6/2014, 3:16:44 AM

Confirmations

5,992,082

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f8f11e489d174305f2da4d2874ffe61ed5b2525914c80baf10d455201b603d38
Transactions (2)
Coinbase4eba1bcbd65d83…1cf54c4e5affdc
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
e89339ca2fe0b0…d59542b5bd72b9
1 in β†’ 2 out0.0940 XPM226 B
AJpuwBaZ…nCW3mtzvARQq5M8b…LDn6ZEEK
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.

4.150 Γ— 10⁹⁢(97-digit number)
41501997303563316242…39618984719223098881
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
4.150 Γ— 10⁹⁢(97-digit number)
41501997303563316242…39618984719223098881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.300 Γ— 10⁹⁢(97-digit number)
83003994607126632484…79237969438446197761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.660 Γ— 10⁹⁷(98-digit number)
16600798921425326496…58475938876892395521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.320 Γ— 10⁹⁷(98-digit number)
33201597842850652993…16951877753784791041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.640 Γ— 10⁹⁷(98-digit number)
66403195685701305987…33903755507569582081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.328 Γ— 10⁹⁸(99-digit number)
13280639137140261197…67807511015139164161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.656 Γ— 10⁹⁸(99-digit number)
26561278274280522394…35615022030278328321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.312 Γ— 10⁹⁸(99-digit number)
53122556548561044789…71230044060556656641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.062 Γ— 10⁹⁹(100-digit number)
10624511309712208957…42460088121113313281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.124 Γ— 10⁹⁹(100-digit number)
21249022619424417915…84920176242226626561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,915,063 XPMΒ·at block #6,833,853 Β· updates every 60s
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