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Block #1,101,769

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/12/2015, 7:39:47 PM Β· Difficulty 10.7593 Β· 5,694,325 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3e9fd43e82387b1e0dd98f350ba03e3859e4a98b882dbe0728b1fac6bada2151
View on Chainz β†—

Height

#1,101,769

Difficulty

10.759286

Transactions

2

Size

572 B

Version

2

Bits

0ac2608a

Nonce

617,895,798

Timestamp

6/12/2015, 7:39:47 PM

Confirmations

5,694,325

Mined by

⛏️ P2SHAdNbEyLbNDXLQYjbKhAhVJXbAU2DUHWi9f

Merkle Root

9a03da4efc24b833b7518775e01b6c385e07642cc2d55aecc74ea38c86934a97
Transactions (2)
Coinbasec54f5fc15bd3d0…3f114b6f623a36
1 in β†’ 1 out8.6300 XPM109 B
AdNbEyLb…2DUHWi9f
6cbc1a4804ca06…cdb5e4d576eaba
2 in β†’ 2 out11.8446 XPM373 B
AHXAxR6f…V7QBgNGAAPaSkzEP…e9f176Qr
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.

2.489 Γ— 10⁹⁴(95-digit number)
24891476610194027397…69643339221993311839
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
2.489 Γ— 10⁹⁴(95-digit number)
24891476610194027397…69643339221993311839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.978 Γ— 10⁹⁴(95-digit number)
49782953220388054794…39286678443986623679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.956 Γ— 10⁹⁴(95-digit number)
99565906440776109589…78573356887973247359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.991 Γ— 10⁹⁡(96-digit number)
19913181288155221917…57146713775946494719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.982 Γ— 10⁹⁡(96-digit number)
39826362576310443835…14293427551892989439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.965 Γ— 10⁹⁡(96-digit number)
79652725152620887671…28586855103785978879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.593 Γ— 10⁹⁢(97-digit number)
15930545030524177534…57173710207571957759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.186 Γ— 10⁹⁢(97-digit number)
31861090061048355068…14347420415143915519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.372 Γ— 10⁹⁢(97-digit number)
63722180122096710137…28694840830287831039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.274 Γ— 10⁹⁷(98-digit number)
12744436024419342027…57389681660575662079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,612,751 XPMΒ·at block #6,796,093 Β· updates every 60s
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