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Block #1,310,695

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/3/2015, 11:35:51 AM Β· Difficulty 10.8489 Β· 5,533,345 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
86874e54c05edb86b8e7bd9bfaa554bb6b4c609a725e1d936bcb7401b6ea7d6c
View on Chainz β†—

Height

#1,310,695

Difficulty

10.848886

Transactions

2

Size

16.71 KB

Version

2

Bits

0ad9509e

Nonce

1,286,204,786

Timestamp

11/3/2015, 11:35:51 AM

Confirmations

5,533,345

Mined by

⛏️ P2SHAUrM8xgiKSsX8DY1QeFbhuayW5foT4jXFQ

Merkle Root

1fd635106e8c4af687ed1314fe8b0d60321dd937b4dbd53bb1b4b5386081fd35
Transactions (2)
Coinbase3350d4968f2b40…31c62789787d0b
1 in β†’ 1 out8.6600 XPM109 B
AUrM8xgi…foT4jXFQ
7266eb28550ca4…b7e38bf3ae0527
114 in β†’ 1 out66.0839 XPM16.52 KB
AQHE5e6H…xDwU3vYU
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.

5.978 Γ— 10⁹⁡(96-digit number)
59788442053139567607…64865127279866972479
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
5.978 Γ— 10⁹⁡(96-digit number)
59788442053139567607…64865127279866972479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.195 Γ— 10⁹⁢(97-digit number)
11957688410627913521…29730254559733944959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.391 Γ— 10⁹⁢(97-digit number)
23915376821255827042…59460509119467889919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.783 Γ— 10⁹⁢(97-digit number)
47830753642511654085…18921018238935779839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.566 Γ— 10⁹⁢(97-digit number)
95661507285023308171…37842036477871559679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.913 Γ— 10⁹⁷(98-digit number)
19132301457004661634…75684072955743119359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.826 Γ— 10⁹⁷(98-digit number)
38264602914009323268…51368145911486238719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.652 Γ— 10⁹⁷(98-digit number)
76529205828018646537…02736291822972477439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.530 Γ— 10⁹⁸(99-digit number)
15305841165603729307…05472583645944954879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.061 Γ— 10⁹⁸(99-digit number)
30611682331207458614…10945167291889909759
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:57,996,689 XPMΒ·at block #6,844,039 Β· updates every 60s
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