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Block #2,257,358

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/18/2017, 2:14:44 PM Β· Difficulty 10.9517 Β· 4,584,977 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c90b06c0684bd316480dc775a2c42651591719f41ac22878132d262bc045a0ee
View on Chainz β†—

Height

#2,257,358

Difficulty

10.951708

Transactions

2

Size

427 B

Version

2

Bits

0af3a327

Nonce

489,892,604

Timestamp

8/18/2017, 2:14:44 PM

Confirmations

4,584,977

Mined by

⛏️ P2SHAdNWGa8Srhv6jf3jFc4rEJ6viWxee195nt

Merkle Root

618c3b28e9e3d65b570b821cffc16bd0530b86cac1a56713f0a7d6b5891adf8f
Transactions (2)
Coinbase55e078cf9dfe2c…b6d8f929386564
1 in β†’ 1 out8.3300 XPM110 B
AdNWGa8S…xee195nt
c52c4b0dc16ce1…53aa004d91c300
1 in β†’ 2 out35819.1487 XPM227 B
AUSgZFhF…wRdCvxp7AUn2Kwfi…R8KZwnsu
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.

3.524 Γ— 10⁹⁴(95-digit number)
35240769130779282397…37650329162571510799
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
3.524 Γ— 10⁹⁴(95-digit number)
35240769130779282397…37650329162571510799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.524 Γ— 10⁹⁴(95-digit number)
35240769130779282397…37650329162571510801
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
7.048 Γ— 10⁹⁴(95-digit number)
70481538261558564794…75300658325143021599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.048 Γ— 10⁹⁴(95-digit number)
70481538261558564794…75300658325143021601
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
1.409 Γ— 10⁹⁡(96-digit number)
14096307652311712958…50601316650286043199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.409 Γ— 10⁹⁡(96-digit number)
14096307652311712958…50601316650286043201
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
2.819 Γ— 10⁹⁡(96-digit number)
28192615304623425917…01202633300572086399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.819 Γ— 10⁹⁡(96-digit number)
28192615304623425917…01202633300572086401
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
5.638 Γ— 10⁹⁡(96-digit number)
56385230609246851835…02405266601144172799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.638 Γ— 10⁹⁡(96-digit number)
56385230609246851835…02405266601144172801
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
1.127 Γ— 10⁹⁢(97-digit number)
11277046121849370367…04810533202288345599
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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