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Block #377,407

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/27/2014, 2:26:02 AM Β· Difficulty 10.4224 Β· 6,429,344 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
da2ffee3389ca6a2b99d04b5664a4bb2b62cb23bb7c85757373fb86359779e2c
View on Chainz β†—

Height

#377,407

Difficulty

10.422442

Transactions

2

Size

539 B

Version

2

Bits

0a6c2528

Nonce

56,440

Timestamp

1/27/2014, 2:26:02 AM

Confirmations

6,429,344

Mined by

⛏️ P2SHAZ7P3QFFTg7Cp4uq5WxADSJ92Rw8VxpSKV

Merkle Root

869423d12afc9bfa20194fccf5f951edd4afff8800d3492336e0aa86ae016c35
Transactions (2)
Coinbase4eac55f27edfda…03d597fe73f878
1 in β†’ 1 out9.2000 XPM109 B
AZ7P3QFF…w8VxpSKV
16e5302dccf560…71f99eff88a77b
2 in β†’ 1 out30.8900 XPM340 B
ALJyTvMK…TKR5uyD8
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.

3.850 Γ— 10⁹⁡(96-digit number)
38501305202364463235…99782122423799667079
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
3.850 Γ— 10⁹⁡(96-digit number)
38501305202364463235…99782122423799667079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.700 Γ— 10⁹⁡(96-digit number)
77002610404728926471…99564244847599334159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.540 Γ— 10⁹⁢(97-digit number)
15400522080945785294…99128489695198668319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.080 Γ— 10⁹⁢(97-digit number)
30801044161891570588…98256979390397336639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.160 Γ— 10⁹⁢(97-digit number)
61602088323783141177…96513958780794673279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.232 Γ— 10⁹⁷(98-digit number)
12320417664756628235…93027917561589346559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.464 Γ— 10⁹⁷(98-digit number)
24640835329513256471…86055835123178693119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.928 Γ— 10⁹⁷(98-digit number)
49281670659026512942…72111670246357386239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.856 Γ— 10⁹⁷(98-digit number)
98563341318053025884…44223340492714772479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.971 Γ— 10⁹⁸(99-digit number)
19712668263610605176…88446680985429544959
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:57,698,107 XPMΒ·at block #6,806,750 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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