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Block #2,787,377

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 8/10/2018, 5:20:02 AM Β· Difficulty 11.6744 Β· 4,054,351 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bef75fadc8bae83cea67c19e3e14842707748eb3b62b984bdafe5585f9d2accc
View on Chainz β†—

Height

#2,787,377

Difficulty

11.674416

Transactions

2

Size

571 B

Version

2

Bits

0baca680

Nonce

71,060,114

Timestamp

8/10/2018, 5:20:02 AM

Confirmations

4,054,351

Mined by

⛏️ P2SHAa75jX7GJBfpttaX29PDfz2YLnbDRA39Xz

Merkle Root

5ea71b30dcb36464c03bb84da5d0a3b68d91c9e8f5c5ccdd771145def93666d9
Transactions (2)
Coinbase31fe3758fc953c…661ab0f9babe1f
1 in β†’ 1 out7.3300 XPM110 B
Aa75jX7G…bDRA39Xz
01d6a9be418d1b…7489d226840235
2 in β†’ 1 out207.4600 XPM371 B
AHFaAReA…jtEZSzFH
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.

1.874 Γ— 10⁹⁡(96-digit number)
18748755844506223763…39093125231516257279
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
1.874 Γ— 10⁹⁡(96-digit number)
18748755844506223763…39093125231516257279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.874 Γ— 10⁹⁡(96-digit number)
18748755844506223763…39093125231516257281
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
3.749 Γ— 10⁹⁡(96-digit number)
37497511689012447527…78186250463032514559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.749 Γ— 10⁹⁡(96-digit number)
37497511689012447527…78186250463032514561
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
7.499 Γ— 10⁹⁡(96-digit number)
74995023378024895055…56372500926065029119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.499 Γ— 10⁹⁡(96-digit number)
74995023378024895055…56372500926065029121
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
1.499 Γ— 10⁹⁢(97-digit number)
14999004675604979011…12745001852130058239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.499 Γ— 10⁹⁢(97-digit number)
14999004675604979011…12745001852130058241
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
2.999 Γ— 10⁹⁢(97-digit number)
29998009351209958022…25490003704260116479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.999 Γ— 10⁹⁢(97-digit number)
29998009351209958022…25490003704260116481
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
5.999 Γ— 10⁹⁢(97-digit number)
59996018702419916044…50980007408520232959
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
5.999 Γ— 10⁹⁢(97-digit number)
59996018702419916044…50980007408520232961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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
Circulating Supply:57,978,205 XPMΒ·at block #6,841,727 Β· updates every 60s
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