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Block #2,665,156

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/17/2018, 11:05:40 AM Β· Difficulty 11.6593 Β· 4,175,181 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
868e954c0e6c5bbf6e829b9d5c6da9bdec46ee18bb8b6bf5dc721c441890bf6a
View on Chainz β†—

Height

#2,665,156

Difficulty

11.659304

Transactions

2

Size

1019 B

Version

2

Bits

0ba8c82b

Nonce

759,587,558

Timestamp

5/17/2018, 11:05:40 AM

Confirmations

4,175,181

Mined by

⛏️ P2SHAHABvSmxzWJktb3S36DeUhLu7MrK8Acmgd

Merkle Root

76ca2b8185dd7bc86e6ec0d85b73d9100b9834028aae69992b1a333b9d281370
Transactions (2)
Coinbase010a1982f16755…ac724d85e4b620
1 in β†’ 1 out7.3500 XPM110 B
AHABvSmx…rK8Acmgd
7516a1b31d32f1…9b668c2169d3d2
5 in β†’ 2 out9975.8901 XPM819 B
AWABuJ36…4G2nqKVHALssV9Qd…PvJB43wd
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.

4.677 Γ— 10⁹³(94-digit number)
46776123709307895328…27658087343276651841
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
4.677 Γ— 10⁹³(94-digit number)
46776123709307895328…27658087343276651841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.355 Γ— 10⁹³(94-digit number)
93552247418615790657…55316174686553303681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.871 Γ— 10⁹⁴(95-digit number)
18710449483723158131…10632349373106607361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.742 Γ— 10⁹⁴(95-digit number)
37420898967446316262…21264698746213214721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.484 Γ— 10⁹⁴(95-digit number)
74841797934892632525…42529397492426429441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.496 Γ— 10⁹⁡(96-digit number)
14968359586978526505…85058794984852858881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.993 Γ— 10⁹⁡(96-digit number)
29936719173957053010…70117589969705717761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.987 Γ— 10⁹⁡(96-digit number)
59873438347914106020…40235179939411435521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.197 Γ— 10⁹⁢(97-digit number)
11974687669582821204…80470359878822871041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.394 Γ— 10⁹⁢(97-digit number)
23949375339165642408…60940719757645742081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.789 Γ— 10⁹⁢(97-digit number)
47898750678331284816…21881439515291484161
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:57,967,017 XPMΒ·at block #6,840,336 Β· updates every 60s
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