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Block #277,695

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/27/2013, 4:21:24 PM Β· Difficulty 9.9670 Β· 6,562,282 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d43c7351daa98ef1bfba02edd798ffbf609c25e5b58952091a20d495c4f12b5e
View on Chainz β†—

Height

#277,695

Difficulty

9.967014

Transactions

2

Size

563 B

Version

2

Bits

09f78e39

Nonce

18,028

Timestamp

11/27/2013, 4:21:24 PM

Confirmations

6,562,282

Mined by

⛏️ <aRMRAbopjr7ZNGrUjb1L7deX9XNozHzLTB81mz

Merkle Root

8230ec7df5b00f7145154a638364ea578f6e528d2d4f0bda4d09ccb727f13dbd
Transactions (2)
Coinbase21582ae621a820…c877c26589012b
1 in β†’ 1 out10.0500 XPM97 B
Abopjr7Z…zLTB81mz
2fe38a72ae3a63…73b7b8a8fa92c7
2 in β†’ 2 out264.3641 XPM375 B
AM8JVVQu…kkY3Y6ccARo32Xqg…2DSaRuZA
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.

1.249 Γ— 10⁹⁢(97-digit number)
12498178364437199041…59180607367448811521
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
1.249 Γ— 10⁹⁢(97-digit number)
12498178364437199041…59180607367448811521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.499 Γ— 10⁹⁢(97-digit number)
24996356728874398083…18361214734897623041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.999 Γ— 10⁹⁢(97-digit number)
49992713457748796166…36722429469795246081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.998 Γ— 10⁹⁢(97-digit number)
99985426915497592332…73444858939590492161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.999 Γ— 10⁹⁷(98-digit number)
19997085383099518466…46889717879180984321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.999 Γ— 10⁹⁷(98-digit number)
39994170766199036933…93779435758361968641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.998 Γ— 10⁹⁷(98-digit number)
79988341532398073866…87558871516723937281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.599 Γ— 10⁹⁸(99-digit number)
15997668306479614773…75117743033447874561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.199 Γ— 10⁹⁸(99-digit number)
31995336612959229546…50235486066895749121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.399 Γ— 10⁹⁸(99-digit number)
63990673225918459093…00470972133791498241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.279 Γ— 10⁹⁹(100-digit number)
12798134645183691818…00941944267582996481
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:57,964,122 XPMΒ·at block #6,839,976 Β· updates every 60s
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