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Block #375,674

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 1/25/2014, 9:15:40 PM Ā· Difficulty 10.4241 Ā· 6,435,223 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8539f1d0a96b3e1c0381ba135be0f39d29d0f2a7c8fea8c0f1eb331a0eac206c
View on Chainz ā†—

Height

#375,674

Difficulty

10.424142

Transactions

1

Size

969 B

Version

2

Bits

0a6c9499

Nonce

23,601

Timestamp

1/25/2014, 9:15:40 PM

Confirmations

6,435,223

Mined by

ā›ļø zaRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

43b77c9b659be563c7422fdc9509ec6b329cab52d33f5bb6b5fe24a74ac7b5bc
Transactions (1)
Coinbase43b77c9b659be5ā€¦fe24a74ac7b5bc
1 in ā†’ 24 out9.1900 XPM879 B
AQvZBsUoā€¦hppgRZTJAFutDVqJā€¦TJTJj6UFAac9Hjdgā€¦P4ktypc3AYtDvcGsā€¦VuAcA7m7AGKhfQo2ā€¦h7fBXLX6
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.

2.525 Ɨ 10ā¹ā“(95-digit number)
25259146556496448597ā€¦87124536648049735679
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
2.525 Ɨ 10ā¹ā“(95-digit number)
25259146556496448597ā€¦87124536648049735679
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
2.525 Ɨ 10ā¹ā“(95-digit number)
25259146556496448597ā€¦87124536648049735681
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
5.051 Ɨ 10ā¹ā“(95-digit number)
50518293112992897195ā€¦74249073296099471359
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
5.051 Ɨ 10ā¹ā“(95-digit number)
50518293112992897195ā€¦74249073296099471361
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
1.010 Ɨ 10ā¹āµ(96-digit number)
10103658622598579439ā€¦48498146592198942719
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
1.010 Ɨ 10ā¹āµ(96-digit number)
10103658622598579439ā€¦48498146592198942721
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
2.020 Ɨ 10ā¹āµ(96-digit number)
20207317245197158878ā€¦96996293184397885439
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
2.020 Ɨ 10ā¹āµ(96-digit number)
20207317245197158878ā€¦96996293184397885441
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
4.041 Ɨ 10ā¹āµ(96-digit number)
40414634490394317756ā€¦93992586368795770879
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
4.041 Ɨ 10ā¹āµ(96-digit number)
40414634490394317756ā€¦93992586368795770881
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:57,731,274 XPMĀ·at block #6,810,896 Ā· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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