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Block #265,042

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 11/19/2013, 5:34:17 AM Ā· Difficulty 9.9633 Ā· 6,547,640 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aede5f57c38a6d3ec025d6e8d9c8d6ebdac21b58a7c564536e311e6a0205bba6
View on Chainz ā†—

Height

#265,042

Difficulty

9.963292

Transactions

5

Size

1.91 KB

Version

2

Bits

09f69a4a

Nonce

139,321

Timestamp

11/19/2013, 5:34:17 AM

Confirmations

6,547,640

Mined by

ā›ļø P2SHALZL8f5Tb3uQncCQYfRsv7qyDAdxKg5v6B

Merkle Root

a224bfbae61d477e043115a7c52584bdf42624bd6a6fdd2d8c2e863e5eb38e58
Transactions (5)
Coinbased97e839e396803ā€¦015a78bbbc3c52
1 in ā†’ 1 out10.1000 XPM109 B
ALZL8f5Tā€¦dxKg5v6B
7c825b11e0f0f1ā€¦7305d095e67560
4 in ā†’ 2 out107.4100 XPM672 B
ANPPuQ8uā€¦XXtkM2btAMBN9TkLā€¦3ymbtNXj
2b7a4b049bdd0dā€¦1f0922f2765212
1 in ā†’ 2 out10.0200 XPM225 B
AJtQEqULā€¦cLE2GkfmAUbLZLUgā€¦F5ME7d7F
ae768f03d67078ā€¦5e8f0c9b5b680b
2 in ā†’ 2 out10.1990 XPM375 B
ALhviLBjā€¦8wz1ovnWAa2JA2Lkā€¦R4Q3S5WK
740bb9b37828fdā€¦77a1801f540b92
3 in ā†’ 1 out7.0235 XPM489 B
AchsxGuoā€¦8P7cTTXE
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.

3.909 Ɨ 10ā¹ā“(95-digit number)
39095414891997971671ā€¦64721649668335530239
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
3.909 Ɨ 10ā¹ā“(95-digit number)
39095414891997971671ā€¦64721649668335530239
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
3.909 Ɨ 10ā¹ā“(95-digit number)
39095414891997971671ā€¦64721649668335530241
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
7.819 Ɨ 10ā¹ā“(95-digit number)
78190829783995943342ā€¦29443299336671060479
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
7.819 Ɨ 10ā¹ā“(95-digit number)
78190829783995943342ā€¦29443299336671060481
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
1.563 Ɨ 10ā¹āµ(96-digit number)
15638165956799188668ā€¦58886598673342120959
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
1.563 Ɨ 10ā¹āµ(96-digit number)
15638165956799188668ā€¦58886598673342120961
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
3.127 Ɨ 10ā¹āµ(96-digit number)
31276331913598377337ā€¦17773197346684241919
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
3.127 Ɨ 10ā¹āµ(96-digit number)
31276331913598377337ā€¦17773197346684241921
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
6.255 Ɨ 10ā¹āµ(96-digit number)
62552663827196754674ā€¦35546394693368483839
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
6.255 Ɨ 10ā¹āµ(96-digit number)
62552663827196754674ā€¦35546394693368483841
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:57,745,490 XPMĀ·at block #6,812,681 Ā· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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