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Block #60,308

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2013, 7:15:56 AM Β· Difficulty 8.9687 Β· 6,748,790 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c1b61b5e02ee39ae06c8ca3d93a6a5a7045fbc354b6ee48af742c4fb01257ef2
View on Chainz β†—

Height

#60,308

Difficulty

8.968667

Transactions

1

Size

200 B

Version

2

Bits

08f7fa8a

Nonce

52

Timestamp

7/18/2013, 7:15:56 AM

Confirmations

6,748,790

Mined by

⛏️ P2SHAMgH7Qy1wZjqkkZTiYj4WXLPRVKvg9qXiM

Merkle Root

e8b79be9e3092cc90fc997973da8161cf7613dd2a37b2a61f4fe2352648a8251
Transactions (1)
Coinbasee8b79be9e3092c…fe2352648a8251
1 in β†’ 1 out12.4100 XPM110 B
AMgH7Qy1…Kvg9qXiM
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.

7.361 Γ— 10⁹³(94-digit number)
73615296888864641897…09754762560830721791
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
7.361 Γ— 10⁹³(94-digit number)
73615296888864641897…09754762560830721791
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.472 Γ— 10⁹⁴(95-digit number)
14723059377772928379…19509525121661443581
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.944 Γ— 10⁹⁴(95-digit number)
29446118755545856759…39019050243322887161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.889 Γ— 10⁹⁴(95-digit number)
58892237511091713518…78038100486645774321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.177 Γ— 10⁹⁡(96-digit number)
11778447502218342703…56076200973291548641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.355 Γ— 10⁹⁡(96-digit number)
23556895004436685407…12152401946583097281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.711 Γ— 10⁹⁡(96-digit number)
47113790008873370814…24304803893166194561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.422 Γ— 10⁹⁡(96-digit number)
94227580017746741629…48609607786332389121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.884 Γ— 10⁹⁢(97-digit number)
18845516003549348325…97219215572664778241
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,716,838 XPMΒ·at block #6,809,097 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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