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Block #1,317,077

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/7/2015, 2:02:51 PM Β· Difficulty 10.8626 Β· 5,499,682 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7f694ebe5687c8df88fdacb44f5b5516dd3de186e5d96cf2229cadd5aa35481c
View on Chainz β†—

Height

#1,317,077

Difficulty

10.862646

Transactions

2

Size

6.77 KB

Version

2

Bits

0adcd65c

Nonce

312,377,146

Timestamp

11/7/2015, 2:02:51 PM

Confirmations

5,499,682

Mined by

⛏️ P2SHAU2R1xf7XKVGsmc21ehrRLzziPB2omGZeV

Merkle Root

9698739bdec6cccefedb507128bfdab710981d9515eb88a843936deb8ffe7a81
Transactions (2)
Coinbased2ab9615366e00…e525cde54f17c9
1 in β†’ 1 out8.6500 XPM110 B
AU2R1xf7…B2omGZeV
daf1bd04075f2d…ccae71d8024ce7
45 in β†’ 2 out427.0389 XPM6.57 KB
ASEL2tNX…58Arw94YAaa8auJM…UVg7ptgZ
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.

3.300 Γ— 10⁹⁢(97-digit number)
33000356583359482594…75834065979607736319
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
3.300 Γ— 10⁹⁢(97-digit number)
33000356583359482594…75834065979607736319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.600 Γ— 10⁹⁢(97-digit number)
66000713166718965189…51668131959215472639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.320 Γ— 10⁹⁷(98-digit number)
13200142633343793037…03336263918430945279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.640 Γ— 10⁹⁷(98-digit number)
26400285266687586075…06672527836861890559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.280 Γ— 10⁹⁷(98-digit number)
52800570533375172151…13345055673723781119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.056 Γ— 10⁹⁸(99-digit number)
10560114106675034430…26690111347447562239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.112 Γ— 10⁹⁸(99-digit number)
21120228213350068860…53380222694895124479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.224 Γ— 10⁹⁸(99-digit number)
42240456426700137721…06760445389790248959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.448 Γ— 10⁹⁸(99-digit number)
84480912853400275442…13520890779580497919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.689 Γ— 10⁹⁹(100-digit number)
16896182570680055088…27041781559160995839
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:57,778,103 XPMΒ·at block #6,816,758 Β· updates every 60s
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