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Block #1,435,089

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 1/29/2016, 6:07:42 PM Ā· Difficulty 10.8100 Ā· 5,381,879 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0446e7384411defa658bb61c3de5e2b4bfc306e434a80b0bb2532ffe88e5d420
View on Chainz ā†—

Height

#1,435,089

Difficulty

10.810038

Transactions

2

Size

1.15 KB

Version

2

Bits

0acf5ea7

Nonce

8,963,806

Timestamp

1/29/2016, 6:07:42 PM

Confirmations

5,381,879

Mined by

ā›ļø P2SHAaXpBr3xCUcp6M2qvxmqkw9rsDKeTd5Rqu

Merkle Root

f07bd1d9554e16148cf386a225bc382e23d4bb6a2411ab38fd97bbcff7b47ee5
Transactions (2)
Coinbase2d5b31939229a4ā€¦a1e38088eb34fb
1 in ā†’ 1 out8.5500 XPM110 B
AaXpBr3xā€¦KeTd5Rqu
ba4298f33a385aā€¦7816ba3052c597
1 in ā†’ 24 out153.5711 XPM974 B
APGdziGWā€¦3ou8jPJiAc3qDtW5ā€¦8bYZSGfWAaYzrf9Yā€¦SsbBAEdLAWzXRhXBā€¦9FxqTxFCAXmDywQVā€¦xDESZZcb
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.443 Ɨ 10ā¹āµ(96-digit number)
14431094525790229777ā€¦29031406506936870239
Discovered Prime Numbers
Lower: 2^k Ɨ origin āˆ’ 1 | Upper: 2^k Ɨ 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 ā€” Twin Prime Pair (origin Ā± 1)
origin āˆ’ 1
1.443 Ɨ 10ā¹āµ(96-digit number)
14431094525790229777ā€¦29031406506936870239
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
1.443 Ɨ 10ā¹āµ(96-digit number)
14431094525790229777ā€¦29031406506936870241
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: origin + 1 āˆ’ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 1 ā€” Twin Prime Pair (2^1 Ɨ origin Ā± 1)
2^1 Ɨ origin āˆ’ 1
2.886 Ɨ 10ā¹āµ(96-digit number)
28862189051580459554ā€¦58062813013873740479
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
2.886 Ɨ 10ā¹āµ(96-digit number)
28862189051580459554ā€¦58062813013873740481
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^1 Ɨ origin + 1 āˆ’ 2^1 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 2 ā€” Twin Prime Pair (2^2 Ɨ origin Ā± 1)
2^2 Ɨ origin āˆ’ 1
5.772 Ɨ 10ā¹āµ(96-digit number)
57724378103160919109ā€¦16125626027747480959
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
5.772 Ɨ 10ā¹āµ(96-digit number)
57724378103160919109ā€¦16125626027747480961
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^2 Ɨ origin + 1 āˆ’ 2^2 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 3 ā€” Twin Prime Pair (2^3 Ɨ origin Ā± 1)
2^3 Ɨ origin āˆ’ 1
1.154 Ɨ 10ā¹ā¶(97-digit number)
11544875620632183821ā€¦32251252055494961919
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
1.154 Ɨ 10ā¹ā¶(97-digit number)
11544875620632183821ā€¦32251252055494961921
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^3 Ɨ origin + 1 āˆ’ 2^3 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 4 ā€” Twin Prime Pair (2^4 Ɨ origin Ā± 1)
2^4 Ɨ origin āˆ’ 1
2.308 Ɨ 10ā¹ā¶(97-digit number)
23089751241264367643ā€¦64502504110989923839
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
2.308 Ɨ 10ā¹ā¶(97-digit number)
23089751241264367643ā€¦64502504110989923841
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^4 Ɨ origin + 1 āˆ’ 2^4 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin ā€” the large number shown above ā€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

ā˜…ā˜…ā˜†ā˜†ā˜†
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 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” 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 āˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
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