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Block #2,837,172

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/13/2018, 8:10:11 AM Β· Difficulty 11.7162 Β· 4,007,316 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f512d92cf59e4180a8b3ddd329bf8900a34ecaba7979b02c255f9734b8b4bed6
View on Chainz β†—

Height

#2,837,172

Difficulty

11.716163

Transactions

1

Size

201 B

Version

2

Bits

0bb75675

Nonce

531,050,384

Timestamp

9/13/2018, 8:10:11 AM

Confirmations

4,007,316

Mined by

⛏️ P2SHAbjo43XTPGoMPDr4hagaBF89MtTnrRXQxQ

Merkle Root

79fa78e05f5fe38bfa27046417c4b2e2ac04eb7ddb8dce464266abda82f5b533
Transactions (1)
Coinbase79fa78e05f5fe3…66abda82f5b533
1 in β†’ 1 out7.2700 XPM110 B
Abjo43XT…TnrRXQxQ
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.

1.917 Γ— 10⁹⁢(97-digit number)
19177973693669852885…39353375865846302719
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
1.917 Γ— 10⁹⁢(97-digit number)
19177973693669852885…39353375865846302719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.835 Γ— 10⁹⁢(97-digit number)
38355947387339705770…78706751731692605439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.671 Γ— 10⁹⁢(97-digit number)
76711894774679411541…57413503463385210879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.534 Γ— 10⁹⁷(98-digit number)
15342378954935882308…14827006926770421759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.068 Γ— 10⁹⁷(98-digit number)
30684757909871764616…29654013853540843519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.136 Γ— 10⁹⁷(98-digit number)
61369515819743529233…59308027707081687039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.227 Γ— 10⁹⁸(99-digit number)
12273903163948705846…18616055414163374079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.454 Γ— 10⁹⁸(99-digit number)
24547806327897411693…37232110828326748159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.909 Γ— 10⁹⁸(99-digit number)
49095612655794823386…74464221656653496319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.819 Γ— 10⁹⁸(99-digit number)
98191225311589646773…48928443313306992639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.963 Γ— 10⁹⁹(100-digit number)
19638245062317929354…97856886626613985279
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:58,000,300 XPMΒ·at block #6,844,487 Β· updates every 60s
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