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Block #2,617,654

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/17/2018, 7:35:10 AM Β· Difficulty 11.2296 Β· 4,187,709 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
880cb42ef9d9eb47340cee94cf25199ea1c46a55eae2033a356d6c7222205b87
View on Chainz β†—

Height

#2,617,654

Difficulty

11.229550

Transactions

2

Size

92.50 KB

Version

2

Bits

0b3ac3cf

Nonce

29,326,123

Timestamp

4/17/2018, 7:35:10 AM

Confirmations

4,187,709

Mined by

⛏️ P2SHAXLEsmW6RpfiBnKmmoXJ6TfJ3iQd9uoEXk

Merkle Root

e47daba13aff503f188b200334f469c9071d52387742d85c86f3e349c4a7a96f
Transactions (2)
Coinbase96d26c7e9fe379…624486c5358919
1 in β†’ 1 out8.8700 XPM110 B
AXLEsmW6…Qd9uoEXk
7a073966eaf83e…fc85a58a47f8ac
638 in β†’ 2 out650.0100 XPM92.30 KB
AU5CF2qx…YAMn2yJ7ALPF8J52…Hjw4BMsG
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.

4.745 Γ— 10⁹⁴(95-digit number)
47453049279576919417…50662301139337879119
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.745 Γ— 10⁹⁴(95-digit number)
47453049279576919417…50662301139337879119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.490 Γ— 10⁹⁴(95-digit number)
94906098559153838834…01324602278675758239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.898 Γ— 10⁹⁡(96-digit number)
18981219711830767766…02649204557351516479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.796 Γ— 10⁹⁡(96-digit number)
37962439423661535533…05298409114703032959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.592 Γ— 10⁹⁡(96-digit number)
75924878847323071067…10596818229406065919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.518 Γ— 10⁹⁢(97-digit number)
15184975769464614213…21193636458812131839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.036 Γ— 10⁹⁢(97-digit number)
30369951538929228426…42387272917624263679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.073 Γ— 10⁹⁢(97-digit number)
60739903077858456853…84774545835248527359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.214 Γ— 10⁹⁷(98-digit number)
12147980615571691370…69549091670497054719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.429 Γ— 10⁹⁷(98-digit number)
24295961231143382741…39098183340994109439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.859 Γ— 10⁹⁷(98-digit number)
48591922462286765483…78196366681988218879
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,686,978 XPMΒ·at block #6,805,362 Β· updates every 60s
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