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Block #2,787,239

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 8/10/2018, 3:14:36 AM Β· Difficulty 11.6736 Β· 4,020,491 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
33e1f88f15c2f3cfa1c4bcea276888ddd314625d130668ad3b6e8d6d5ab32bc9
View on Chainz β†—

Height

#2,787,239

Difficulty

11.673557

Transactions

2

Size

1.86 KB

Version

2

Bits

0bac6e3e

Nonce

685,166,057

Timestamp

8/10/2018, 3:14:36 AM

Confirmations

4,020,491

Mined by

⛏️ P2SHAPNKt1hPDX5vJJWFRRNALco5XhULB68VgL

Merkle Root

e9cc443054845a978fc8c75456778bf648dc527f2368d12dea7b3f26fb968478
Transactions (2)
Coinbase0ecea4fd44170e…0b6117b024e1c9
1 in β†’ 1 out7.3700 XPM109 B
APNKt1hP…ULB68VgL
b5c6c4edf72ee2…154394f8eacc15
11 in β†’ 2 out12486.5871 XPM1.67 KB
AMzVG56m…QkgEyBkbAPxKcc3b…CDSJELKX
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.

7.413 Γ— 10⁹⁢(97-digit number)
74131286714521945782…94194351139673159679
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
7.413 Γ— 10⁹⁢(97-digit number)
74131286714521945782…94194351139673159679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.413 Γ— 10⁹⁢(97-digit number)
74131286714521945782…94194351139673159681
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
1.482 Γ— 10⁹⁷(98-digit number)
14826257342904389156…88388702279346319359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.482 Γ— 10⁹⁷(98-digit number)
14826257342904389156…88388702279346319361
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
2.965 Γ— 10⁹⁷(98-digit number)
29652514685808778313…76777404558692638719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.965 Γ— 10⁹⁷(98-digit number)
29652514685808778313…76777404558692638721
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
5.930 Γ— 10⁹⁷(98-digit number)
59305029371617556626…53554809117385277439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.930 Γ— 10⁹⁷(98-digit number)
59305029371617556626…53554809117385277441
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
1.186 Γ— 10⁹⁸(99-digit number)
11861005874323511325…07109618234770554879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.186 Γ— 10⁹⁸(99-digit number)
11861005874323511325…07109618234770554881
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
2.372 Γ— 10⁹⁸(99-digit number)
23722011748647022650…14219236469541109759
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
2.372 Γ— 10⁹⁸(99-digit number)
23722011748647022650…14219236469541109761
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:57,705,874 XPMΒ·at block #6,807,729 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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