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Block #2,781,939

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/6/2018, 4:13:35 PM Β· Difficulty 11.6520 Β· 4,061,294 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bb2826698069697ddb815d2a9d9f43c5091b8f977d0b22037cbe1a0a312a7554
View on Chainz β†—

Height

#2,781,939

Difficulty

11.652010

Transactions

1

Size

200 B

Version

2

Bits

0ba6ea1f

Nonce

129,974,131

Timestamp

8/6/2018, 4:13:35 PM

Confirmations

4,061,294

Mined by

⛏️ P2SHATqmx3mE2DPWCV5RLfRf4PCPSA2Ey4Uayd

Merkle Root

1da5c064566c3097b2a440505f9a0a6fa5fa02ed9418d9d01ec7d31b7b00f4a8
Transactions (1)
Coinbase1da5c064566c30…c7d31b7b00f4a8
1 in β†’ 1 out7.3500 XPM110 B
ATqmx3mE…2Ey4Uayd
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.

1.562 Γ— 10⁹⁴(95-digit number)
15620350237391648356…71812677319552777821
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
1.562 Γ— 10⁹⁴(95-digit number)
15620350237391648356…71812677319552777821
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.124 Γ— 10⁹⁴(95-digit number)
31240700474783296712…43625354639105555641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.248 Γ— 10⁹⁴(95-digit number)
62481400949566593424…87250709278211111281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.249 Γ— 10⁹⁡(96-digit number)
12496280189913318684…74501418556422222561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.499 Γ— 10⁹⁡(96-digit number)
24992560379826637369…49002837112844445121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.998 Γ— 10⁹⁡(96-digit number)
49985120759653274739…98005674225688890241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.997 Γ— 10⁹⁡(96-digit number)
99970241519306549479…96011348451377780481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.999 Γ— 10⁹⁢(97-digit number)
19994048303861309895…92022696902755560961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.998 Γ— 10⁹⁢(97-digit number)
39988096607722619791…84045393805511121921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.997 Γ— 10⁹⁢(97-digit number)
79976193215445239583…68090787611022243841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.599 Γ— 10⁹⁷(98-digit number)
15995238643089047916…36181575222044487681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
3.199 Γ— 10⁹⁷(98-digit number)
31990477286178095833…72363150444088975361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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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