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Block #902,504

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/20/2015, 9:46:04 AM Β· Difficulty 10.9401 Β· 5,894,056 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fb3ebe4bf490b723f2d42604eeeb5e506ab822bf718992295a1136b312df620f
View on Chainz β†—

Height

#902,504

Difficulty

10.940067

Transactions

2

Size

1.87 KB

Version

2

Bits

0af0a83d

Nonce

1,153,785,366

Timestamp

1/20/2015, 9:46:04 AM

Confirmations

5,894,056

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

35bea104e03a32c9a4b61129ebf816670f337da5e924bb600d16f0c5cb443b38
Transactions (2)
Coinbased40253abcf25aa…5d31e9f769eadf
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
54a7bb1d188322…bb5410e1d97d52
11 in β†’ 2 out2140.0700 XPM1.67 KB
Acmayd8S…r7w8Xtr9AXgTS7mk…NBMGi1A6
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.

2.854 Γ— 10⁹⁡(96-digit number)
28544921612203493503…25151597673991768959
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
2.854 Γ— 10⁹⁡(96-digit number)
28544921612203493503…25151597673991768959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.708 Γ— 10⁹⁡(96-digit number)
57089843224406987007…50303195347983537919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.141 Γ— 10⁹⁢(97-digit number)
11417968644881397401…00606390695967075839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.283 Γ— 10⁹⁢(97-digit number)
22835937289762794802…01212781391934151679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.567 Γ— 10⁹⁢(97-digit number)
45671874579525589605…02425562783868303359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.134 Γ— 10⁹⁢(97-digit number)
91343749159051179211…04851125567736606719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.826 Γ— 10⁹⁷(98-digit number)
18268749831810235842…09702251135473213439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.653 Γ— 10⁹⁷(98-digit number)
36537499663620471684…19404502270946426879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.307 Γ— 10⁹⁷(98-digit number)
73074999327240943369…38809004541892853759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.461 Γ— 10⁹⁸(99-digit number)
14614999865448188673…77618009083785707519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.922 Γ— 10⁹⁸(99-digit number)
29229999730896377347…55236018167571415039
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:57,616,479 XPMΒ·at block #6,796,559 Β· updates every 60s
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