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Block #1,312,409

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 11/4/2015, 2:11:43 PM Ā· Difficulty 10.8524 Ā· 5,505,412 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9065698d862cdf8fee9edd21356361f9c83684cf2185f6f1ed2e07998ca2bbd5
View on Chainz ā†—

Height

#1,312,409

Difficulty

10.852411

Transactions

2

Size

1004 B

Version

2

Bits

0ada37a3

Nonce

993,016,528

Timestamp

11/4/2015, 2:11:43 PM

Confirmations

5,505,412

Mined by

ā›ļø P2SHAbGnoehLsEKpgWKbRKCjsdgrxpTkTtzc42

Merkle Root

f056df9921946bf65dc0c61ecd33a73d71e6c443a200f79fa1f50476d36806a8
Transactions (2)
Coinbasef2643ddf8782fcā€¦ffc373e5d1e424
1 in ā†’ 1 out8.4900 XPM110 B
AbGnoehLā€¦TkTtzc42
c048e0cc2f0588ā€¦25c43cca0d13a2
1 in ā†’ 19 out182.7436 XPM804 B
AcGTm5jAā€¦WguFZ9XwAZ4PRBr5ā€¦vRa8ySfzAcyWLcPWā€¦MBkw4RHaALv1DJa5ā€¦8D45HmMrAR3dQ8Pfā€¦TZpRdxnE
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.

5.765 Ɨ 10ā¹ā“(95-digit number)
57658924034654366369ā€¦41132723824584769279
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
5.765 Ɨ 10ā¹ā“(95-digit number)
57658924034654366369ā€¦41132723824584769279
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
5.765 Ɨ 10ā¹ā“(95-digit number)
57658924034654366369ā€¦41132723824584769281
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
1.153 Ɨ 10ā¹āµ(96-digit number)
11531784806930873273ā€¦82265447649169538559
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
1.153 Ɨ 10ā¹āµ(96-digit number)
11531784806930873273ā€¦82265447649169538561
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
2.306 Ɨ 10ā¹āµ(96-digit number)
23063569613861746547ā€¦64530895298339077119
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
2.306 Ɨ 10ā¹āµ(96-digit number)
23063569613861746547ā€¦64530895298339077121
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
4.612 Ɨ 10ā¹āµ(96-digit number)
46127139227723493095ā€¦29061790596678154239
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
4.612 Ɨ 10ā¹āµ(96-digit number)
46127139227723493095ā€¦29061790596678154241
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
9.225 Ɨ 10ā¹āµ(96-digit number)
92254278455446986190ā€¦58123581193356308479
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
9.225 Ɨ 10ā¹āµ(96-digit number)
92254278455446986190ā€¦58123581193356308481
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
Circulating Supply:57,786,631 XPMĀ·at block #6,817,820 Ā· updates every 60s
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