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Block #2,877,604

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/12/2018, 4:30:49 AM Β· Difficulty 11.6481 Β· 3,964,386 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
007a60d09c3f7e427c8440959333db6f1c66eabf176c431ba24dcb6f20bba19d
View on Chainz β†—

Height

#2,877,604

Difficulty

11.648091

Transactions

1

Size

200 B

Version

2

Bits

0ba5e949

Nonce

15,050,487

Timestamp

10/12/2018, 4:30:49 AM

Confirmations

3,964,386

Mined by

⛏️ P2SHAXnS3rFMrNyWRZLHTZc5uL5UzTUkVNnqkP

Merkle Root

9bd40b2a5b0e6b040e3bb6194279fbed1e47dadc419c60db5c5c6f47e6a3868d
Transactions (1)
Coinbase9bd40b2a5b0e6b…5c6f47e6a3868d
1 in β†’ 1 out7.3600 XPM110 B
AXnS3rFM…UkVNnqkP
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.

2.430 Γ— 10⁹⁡(96-digit number)
24304372451777687387…96251098043218820479
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.430 Γ— 10⁹⁡(96-digit number)
24304372451777687387…96251098043218820479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.430 Γ— 10⁹⁡(96-digit number)
24304372451777687387…96251098043218820481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
4.860 Γ— 10⁹⁡(96-digit number)
48608744903555374774…92502196086437640959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.860 Γ— 10⁹⁡(96-digit number)
48608744903555374774…92502196086437640961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
9.721 Γ— 10⁹⁡(96-digit number)
97217489807110749549…85004392172875281919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.721 Γ— 10⁹⁡(96-digit number)
97217489807110749549…85004392172875281921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.944 Γ— 10⁹⁢(97-digit number)
19443497961422149909…70008784345750563839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.944 Γ— 10⁹⁢(97-digit number)
19443497961422149909…70008784345750563841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.888 Γ— 10⁹⁢(97-digit number)
38886995922844299819…40017568691501127679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.888 Γ— 10⁹⁢(97-digit number)
38886995922844299819…40017568691501127681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
7.777 Γ— 10⁹⁢(97-digit number)
77773991845688599639…80035137383002255359
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
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