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Block #324,273

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 12/22/2013, 5:10:44 AM Ā· Difficulty 10.2081 Ā· 6,479,398 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a7a883e8a90e191ca174a792ffbefda411dd37f2b1466b316a604dd9c645d4fb
View on Chainz ā†—

Height

#324,273

Difficulty

10.208115

Transactions

1

Size

837 B

Version

2

Bits

0a35470e

Nonce

64,714

Timestamp

12/22/2013, 5:10:44 AM

Confirmations

6,479,398

Mined by

ā›ļø aRvAP7nJS9VM8BgygCWUvXbEU8t5mLay59hK5

Merkle Root

e42d15462a42948a91ced93b0893ddd22632006f69ddd775a2715e8ca6035e93
Transactions (1)
Coinbasee42d15462a4294ā€¦715e8ca6035e93
1 in ā†’ 20 out9.5756 XPM743 B
AP7nJS9Vā€¦Lay59hK5Aac9Hjdgā€¦P4ktypc3AQwd2tMyā€¦CzytqW6xAdwTEXyCā€¦NwbVbqZVAd9pSzHtā€¦cpJ3y2zz
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.

2.031 Ɨ 10Ā¹ā°ā“(105-digit number)
20314247743399237950ā€¦54551633692853478399
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
2.031 Ɨ 10Ā¹ā°ā“(105-digit number)
20314247743399237950ā€¦54551633692853478399
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
2.031 Ɨ 10Ā¹ā°ā“(105-digit number)
20314247743399237950ā€¦54551633692853478401
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
4.062 Ɨ 10Ā¹ā°ā“(105-digit number)
40628495486798475900ā€¦09103267385706956799
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
4.062 Ɨ 10Ā¹ā°ā“(105-digit number)
40628495486798475900ā€¦09103267385706956801
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
8.125 Ɨ 10Ā¹ā°ā“(105-digit number)
81256990973596951800ā€¦18206534771413913599
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
8.125 Ɨ 10Ā¹ā°ā“(105-digit number)
81256990973596951800ā€¦18206534771413913601
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
1.625 Ɨ 10Ā¹ā°āµ(106-digit number)
16251398194719390360ā€¦36413069542827827199
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
1.625 Ɨ 10Ā¹ā°āµ(106-digit number)
16251398194719390360ā€¦36413069542827827201
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
3.250 Ɨ 10Ā¹ā°āµ(106-digit number)
32502796389438780720ā€¦72826139085655654399
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
3.250 Ɨ 10Ā¹ā°āµ(106-digit number)
32502796389438780720ā€¦72826139085655654401
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:57,673,405 XPMĀ·at block #6,803,670 Ā· updates every 60s
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